Math problem

Question

If $10,000 is invested at an interest rate of 3% per year, compounded semiannually. Find the value of the investment after (a) 5 years? (b) 15 years?

Answer 1

The equation for Future Value with compound interest is:
 
FV=P·(1+r/n)^nt

where:
FV = future value
P = principal (that is, the original investment, = $10,000)
r = annual interest rate (3% = 0.03)
n = frequency of compounding per year (in this case, each 6 months = 2 times per year)
t = number of years

 

So, for the first part, t will equal 5 years

and the formula will be FV = $10,000 · (1 + 0.03/2)^2·5

which becomes FV = $10,000 · (1.015)¹⁰

so, FV = $10,000 · 1.605 ≅ $11,605

 

For the second part, t will equal 15 years

and the formula will be FV = $10,000 · (1.015)^2·15

so, FV = $10,000 · 1.5630 ≅ $15,630