On the day of their son’s birt
On the day of their son’s birth, Mr. and Mrs. Su decided to setaside a sum of
money to provide for his college education. They wish to make asingle deposit in a bank that pays 9% compounded annually in orderto 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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Answer:
According to given information first we need to find the presentvalue of 4 payments at the age of 18,19 20 and 21st. sofirst we need to find the present value of annual payments by usingthe 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 accumulatedvalue of the sum aside by Mr and Mrs Su with a single deposit for17 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
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