Question

A father wants to know How do I invest 548,891 now so that my daughter gets $800 per month of income for the next 12 years? Calculate the answer for this dad. The interest rate of this investment should be % per month. (Round to two decimal places.)

Answer 1

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.