anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous

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mathstudent55
  • mathstudent55
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
  • mathstudent55
\(\large F = P \left(1 + \dfrac{r}{n}\right)^{nt} \) 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
  • mathstudent55
Plug in all your numbers in the formula, and solve for P, the present value.
anonymous
  • anonymous
but its a deffred annuity @mathstudent55
mathstudent55
  • mathstudent55
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
  • anonymous
i got the answer thanks guys :)

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