The following relation is used in problems like these :
P = A* [(1+i)^n - 1]/[i*(1+i)^n]
Where P = Principal Amount
i = rate of interest per year ( in case of monthly calculation i = i/12 and n =12*n)
A = equal withdrawals/instalments = 800 $
P = 48,981 $
Hence ;
Note : Here we have divided i/12 and have multiplied 12 in i^n as the rate on interest needs to calculated on a monthly basis.
48981 = 800*[(1+i/12)^(12*12) - 1]/[i/12(1+i/12)12*12]
[(1+i/12)12*12 - 1]/[i/12(1+i/12)12*12] = 61.22
- 1 = (1+i/12)^144 *[ 61.22i/12 - 1]
we get the value of i =0.1702 which is the monthly rate of interest.
i =0.1702*100 =17.02% is the rate of interest per month in percent.
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