There is an ambiguity in the question to be clarified about the interest rate.
Generally annual interest is quoted. The wording of the question casts a doubt as to 7.2% is monthly or annual interest.
Considering that 86.4% annual interest is illegal in some countries, 7.2% will be considered annual interest.
The monthly payment can be calculated by equating future values and simplification using factorization:
P(1+r)^n = M(1+r+r^2+...+r^(n-1))
=M((1+r)^n-1)/((1+r)-1)
=M((1+r)^n-1)/r
P=present value
M=monthly payment
r=interest per period (month)
n=number of periods (month)
Solve for M:
M=Pr(1+r)^n/((1+r)^n-1)
substituting n=36, r=7.2%/12=0.006,P=15000,
M=15000*0.006*(1.006^36)/(1.006^36-1)
=464.53
Rough check:
For short terms (under 10 years) the total amount paid should cost a little more than the simple interest paid over half the period.
15000*(1+3(years)/2*0.072)=16620
464.53*36=16723 slightly >16620
so ok.
I will leave it to you to tackle the other periods. Post your answer for checking if you wish.
Suppose you borrowed $15000 to buy a car at an interest rate 7.2% compounded monthly. What will the monthly payments be on loans of 36, 48 and 60 months if you do not have to put any money down on the financing?
1 answer