On the day of their son’s birth, Mr. and Mrs. Su decided to set aside a...

On the day of their son’s birth, Mr. and Mrs. Su decided to set aside a sum of

money to provide for his college education. They wish to make a single deposit in a bank that pays 9% compounded annually in order to provide a payment of $12,999 on each of the son’s 18 th, 19th, 20th, 21st birthdays. How much should they deposit?

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Solutions

Expert Solution

According to given information first we need to find the present value of 4 payments at the age of 18,19 20 and 21^st. so first we need to find the present value of annual payments by using the below formula.

Pmt = Periodic monthly payment = 12999

i = Mortgage interest rate per period = 9% = 0.09

n = Number of payments = 4

we can use below formula

PV = Pmt x [(1 - 1 / (1 + i)ⁿ)] / i

PV = 12999 x [(1 - 1 / (1 + 0.09)⁴)] / (0.09)

PV = 12999 X [(1-1/(1.09)⁴)]/(0.09)

PV = 12999 X [1-1/(1.41158)]/(0.09)

PV = 12999 X [1-0.70842]/(0.09)

PV = 12999 X [0.29158]/(0.09)

PV = 12999 X 3.23977

PV = 42113.77 ~ 42114

So the present value of annuity = $42114

Now present value of above annuity is equal to the accumulated value of the sum aside by Mr and Mrs Su with a single deposit for 17 years with a annual compound of 9%

So we can use compound interest formula

A = P (1+r)ⁿ

42114 = P(1+0.09)¹⁷

42114 = P(1.09)¹⁷

42114 = P(4.32763)

P = 42114 / 4.32763

P = 9731.423 ~ 9731.4

So the required initial deposit at the birth of their son is $ 9731.4

Colby Messinger answered 2 years ago

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