Question

Calculate the accumulated value after ten years of payments of $13200.00 made at the end of each month if interest is 4.5% compounded semi-annually.

Answer 1

Future value of annuity = P * [ (1+r)^n - 1] / r

Where, r = rate of interest

P = Payment

n = Number of periods

Interest rate per year = 4.5%

Compounding = 2

So, Interest Per period = 4.5% /2

= 2.25%

Annual Interest rate Effective = ( 1 +r)^m

Where, r is interest per period and m is Number of compounding

= ( 1 +2.25%)^2 - 1

= 1.0455062 - 1

= 0.0455062 or 4.55062%

Monthly Effective rate = ( 1 + Annual rate) ^ (1 / 12) - 1

= ( 1 + 4.55062%)^ (1/12) - 1

= 1.0455062^(1/12) - 1

= 0.003715315 or 0.37153155%

Number of payments = 10*12 [Years * Number of months in a year]

= 120

Future Value = 13200 * [ (1 +0.37153155%)^120 - 1 ] / 0.37153155%

= 13200 * [ (1.0037153155)^120 - 1] / 0.0037153155

= 13200 * (1.56050844 - 1) / 0.0037153155

= 13200 * 150.86429

= 1991408.647

Future Value = 1991408.647