10000 is invested in an account which pays an annual interes

$10,000 is invested in an account which pays an annual interest rate of 5% compounded monthly. what is the value of the investment after 30 months?

Solution

The formula for compound interest, where interest is compounded monthly, is F = P(1 +r/12)ⁿ where P is the principal/initial investment, r is the annual interest rate in decimals , n is the number of months and F is the maturity value. here, P = $ 10000, r = 5/100 = 0.05 ( so that r/12 = 0.05/12 = 0.0041666666666... = 0.004167 approx). Then F =10000 ( 1+ 0.004167)³⁰ = 10000(1.004167)³⁰ = 10000* 1.132865 = $11328.65 ( on rounding off to the nearest cent)