Question

Find i​ (the rate per​ period) and n​ (the number of​ periods) for the following loan at the given annual rate. Monthly payments $316.20 are made for 9 years to repay a loan at 8.35% compounded monthly. I=? Type an integer or decimal rounded to four decimal places as​ needed

Answer 1

SOLUTION:

From given data,

Monthly payments $316.20 are made for 9 years to repay a loan at 8.35% compounded monthly.

Considering the question

%

Here, PMT = the monthly payment,

I = the annual rate

t = the time  period in year.
Using the formula

n= t(m)

i= I/N

Here, N = number of periods

m = the total number of month in the given time period

i= the rate per period

Here the interest compounds monthly. The rate given in the question is for one year. In one year there are 12 periods. Therefore the number of periods in 9 years is

n=9(12)

= 108

Here the interest compounds monthly. The rate given in the question is for one year.In one year there are 12 periods. Therefore the rate per period is

i= 8.35/(100*12)

= 0.007

= 0.7%

The rate per period is 0.7%. The total number of periods are 108.