Question

you owe your best friend $2000. because you are short on cash, you offer to repay the loan over 12 months under the following condition. the first payment will be $100 at the end of month one. the second payment will be $100+G at the end of month two. at the end of month three, you'll repay $100+2G. this pattern of increasing G amounts will continue for all remaining months.
a. what is the value of G if the interest rate is 0.5 per month?
b. what is the equivalent uniform monthly payment?
c. repeat part (a) when the first payment is $150 (i.e., determine G)

Answer 1

a

We know that

Total loan today = 2000

Here it is difficult to understand that the interest rate is 0.5 or 0.5 per cent

I am solving this question as an interest of 0.5% please let me know in comments if you need it to solve as 0.5 per month

Now,

To solve this question we will use excel and create a model as follows

Now,

As we can see that the payment G = 13.258

But to get this number we did iteration

The first column is the serial number

The second column is the amount left which is calculated using the formula

Amount left = The amount left in the previous month - Fix payment - nG + Interest

Interest is calculated using the following formula

Interest = Amount due * 0.005

After doing multiple iterations we can find the value of G

b

This question can be solved using the formula PMT in excel

The inputs are as follows

rate = 0.005

nper = 12

PV = -2000

The output

PMT = 172.13

Thus the uniform monthly payment to pay the loan is 172.13

c

The question can be solved by the same model used to solve part a. However, at the place of 100, we use 150 as fixed payment and therefore the value of G will be as follows

Hence, G = 4.068