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Determine the Required Savings to Reach a Financial Goal - YouTube
Channel: Mathispower4u
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welcome to a lesson on determining the
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regular savings amount needed to reach a
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financial goal
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in this video we'll use the value of an
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annuity formula to achieve a financial
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goal through a regular savings plan
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if we solve the formula here
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used to determine the value of an
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annuity a
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for the value p
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where p is the regular deposit amount
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we would have this formula here where p
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will give us the regular savings amount
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needed to reach
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our financial goal of a
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let's quickly show how we can solve this
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equation for p
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if we multiply both sides by r over n
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this would simplify out
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we'd be left with a times r over n
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equals p
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times the quantity of one plus r over n
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to the nt power
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minus one and now to solve for p we can
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just divide by this quantity here
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and the right side simplifies nicely so
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now we have p equals this fraction here
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which is the formula that we can use to
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determine our regular savings amount to
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reach our financial goal of a let's go
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ahead and give it a try
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let's say you want to purchase a car in
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four years and you want to pay cash for
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the car and have determined that it will
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cost fifteen thousand five hundred
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dollars
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if you are going to make monthly
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deposits into an account that pays six
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percent interest compounded monthly what
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would be the amount of the monthly
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deposits
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and how much interest would you earn
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over this period
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so in this case our monthly payment p
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required to reach our financial goal of
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fifteen thousand five hundred dollars
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which is a
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multiply this by r over n where r is our
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interest rate so .06
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divided by n which is the number of
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compounds per year
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it's monthly so n is 12.
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and we'll divide this by
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one plus
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.06 divided by 12
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all raised to the n times t power we
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just said n was 12 t is time in years
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and we're saving for four years
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so it's 12 times four
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minus one
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let's go and evaluate this on our
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calculator
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so our numerator is going to be 15500
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times .06 divided by 12.
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so there's our numerator
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divided by
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our denominator
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one
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plus .06 divided by 12.
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this will be raised to the power of 12
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times four that'll be 48
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minus one
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and then close parenthesis for our
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denominator
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so we'll have to save 286 dollars and
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approximately 52 cents per month
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if we want to pay cash for this car
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now the second part asks us how much
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interest would we earn over this four
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year period
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we'll pay this amount
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12 times a year for four years so that
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value would represent the amount paid
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into the account
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so to figure this out
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we'll take the ending account balance
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which is fifteen thousand five hundred
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well we deposited two hundred eighty-six
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dollars and fifty-two cents
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every month so it'll be times 12 for the
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number of months per year
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x 4 for the number of years
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so we would earn one thousand seven
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hundred forty-seven dollars and four
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cents in interest over this four-year
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period
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now for the second example we'll look at
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the same problem but just change the
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time frame for the savings so the only
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difference on this problem here is that
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you're going to save for two years
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instead of four years
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so the formula will be exactly the same
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except now t will be equal to two
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so we'll have 12 times two as our
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exponent here
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now let's go back to our calculator and
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see how much more we're going to have to
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save if we only save for two years
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there's our numerator
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our exponent here is going to be 12
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times two that'll be 24.
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and there's our denominator
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so now if we only say for 2 years we
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have to save
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609.47 per month which will obviously be
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a lot more difficult to do
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now let's go and determine how much
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interest would be earned over the
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two-year period compared to the
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four-year period
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so the ending account balance is still
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going to be 15 500
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but our payments
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are only over two years now so we'll
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have the monthly savings amount
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x
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12 payments per year
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times
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two years
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so over the two year period we only
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earned 872.78
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cents
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so this really begins to illustrate the
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power of compounded interest as you
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probably all know cars are not a very
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good investment cars depreciate on
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average of 15 percent per year
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according to carsdirect.com
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so really you could save quite a bit of
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money by purchasing a used car instead
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of a brand new car maybe not this car
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pictured here but you probably could
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save a considerable amount of money i
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hope you found this video helpful thank
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you for watching
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you
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