Question

In: Advanced Math

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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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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