A father wishes to provide P40,000 for his son on his son’s 21st birthday. How much should he deposit every 6 months in a savings account which pays 3% compounded semi-annually, if the first deposit was made when the son was 3 ½ years old?

Question

anonymous · Answer

@mathstudent55

anonymous · Answer

@ganeshie8

anonymous · Answer

@goformit100

mathstudent55 · Answer

The interest rate is 3% per year compounded 2 times per year.
The time is 21 - 3.5 years = 17.5 years
The future amount is P40,000

We need the formula for compound interest, and then to solve it for present value.

mathstudent55 · Answer

$\large F = P \left(1 + \dfrac{r}{n}\right)^{nt} $

where F = future value
P = present value
r = annual interest rate written as a decimal
n = number of compounding periods per year
t = number of years

mathstudent55 · Answer

Plug in all your numbers in the formula, and solve for P, the present value.

anonymous · Answer

but its a deffred annuity  @mathstudent55

mathstudent55 · Answer

Sorry. You are correct. That is the formula if you made a single deposit now (present value), and you want a future value later.
For an annuity, there is a different formula.

$F = A\times \dfrac{n(1 + \frac{r}{n})^{nt} - n }{r } $

where r = decimal interest rate
n = number of compoundings per year
t = number of years
A = periodic payment
F = future value

anonymous · Answer

i got the answer thanks guys :)