Question

please, i need help with the answer thank you

6.3(3)

At the end of each month, for 36 months, $500 is put into an account paying 9 % annual interest compounded continuously. Find the future value of this account. Round your answer to the nearest cent.

Answer 1

Solution

The solution has been worked out as follows, using the given information

Amount deposited each month = $ 500

Period (n) = 36 months

Interest per annum = 9%

Interest per month (i) = 9% / 12

= 0.75% or 0.0075

Future Value Interest Factor of Annuity = {[(1 + i) ^ n ] - 1} / i

= { [ (1 + 0.0075) ^ 36 ] - 1 } / 0.0075

= [1.3086 - 1] / 0.0075

= 41.1467 (Approx)

Future value of Investment = Periodical Investment X Future Value Annuity Factor (As Computed)

= $ (500 X 41.1467)

= $ 20,573.35 or $ 20,573 (Approx)

Answer: Future value of the monthly investment of $ 500 for 36 months at a rate of 9% will be $ 20,573