Question

Determine the interest rate needed to accumulate the following amounts in a sinking fund, with monthly payments as given.

Accumulate $155,000, monthly payments of $500 over 16 years.

Answer 1

Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period =$500
i = interest rate per period
n=number of period =12*16 =196
$155000= $500[ (1+ i)^192 -1] / i
155000/500 =[ (1+ i)^192 -1] / i
310 =[ (1+ i)^192 -1] / i
i=0.4679235%
Monthly rate = 0.4679235%
APR = 0.4679235%*12
=5.62%