Question

Betty DeRose is going to deposit $16,000 into a savings account at the beginning of every six months for the next eight years. Assume the savings account will earn 10% interest compounded semi-annually. Calculate the amount of interest Betty DeRose will earn over the eight year period. Use the time value of money factors

Answer 1

PMT = Payment =	$16,000.00
N = Period = 8 years x 2 semi-annual payments =	16
R = Rate Semi-annual compounding = 10%/2 =	5%
Future value formula for investment done beginning of period:
FV = (PMT x ((1+R/12)^N-1)/R) x (1+R/12)
FV = 16000*((1+10%/2)^16-1)/(10%/2)*(1+10%/2) =	$397,445.86
Total Interest = FV - PMT x N = 397445.86 - 16000 x 16 =	$141,445.86

Hence, Betty DeRose earns $141,445.86 total interest

(Time value annunity factor is 24.8403664 therefore we will get same result by =24.8403664*16000 = FV = $397,445.86 )

Please let me know if you want more explanation for this.