A man buys furniture amounting to R25000 on hire purchase at a flat rate of 7% pa. S. I. He makes a 15% down payment immediately and then repays the loan by means of regular equal instalments at the end of each month for the next nine months. The equivalent, effective annual rate of compound interest on the loan is equal to:

Question

anonymous · Answer

Hi - ans according to my calculation is 0.065% is the effective monthly rate of compound interest and 1.08% is the effective annual rate of compound interest. 

How I got there is this:

Loan amount given: R25000
Simple Interest charged: 7%
Amt immediately paid off as down payment: 3750 (15% of R25000)
Amt remaining: R21250 (R25000-3750)
Total yearly interest to be paid on it: R1750 (7% of 21250)
Total he needs to pay off: R23000 (Interest of 1750 plus principal of 21250)
Therefore monthly installment man would need to pay if he were to pay it in 12 instalments: R1916.66
But since he pays it off in 7 installments he pays per month: R2555.5

Now inputting it into the equation of compound interest

P(11+r)^12 = Principal + Interest
= 21250(1+r)^12 = 23000
= (1+r)^12 = 23000/21250
= 1.08

This means that the effective annual compound interest rate is 1.08% 
If you solved for r you would get the effective monthly rate which is 0.65%

Hope that helped. If I'm wrong, please correct me. Thanks.