Question

Melissa is a very successful clothes designer who is currently selling clothes on the internet. She wants to expand her business and needs a loan to buy sewing machines, fabric and other material, and hire two seamstresses to help her with the sewing. The bank offers her a loan of $400,000 to be paid over 4 years (starting next month) with monthly payments at 6% APR with quarterly compounding. However, Melissa wishes to pay off her debt more quickly and decides to pay each month twice the amount required by the bank. Approximately how many months will it take Melissa to pay off her loan? Hint: You need to first find the monthly payments required by the bank.
Select one:
a. 39.2 months
b. 22.6 months
c. 32.3 months
d. 28.5 months
e. 24 months

Answer 1

The Loan amount was = 400,000

APR rate 6% compounded quarterly

So EIR effective rate = (1+i/m)^m -1

EIR = 6.136% pa

So the original monthly payments

Monthly payment = P*(i/m)   / ( 1- (1+i/m) –mt

Where p = principal

I = interest rate

M= no of compounding

T = time

So

Monthly payment = 400000 * (0.06136/12) / 1-(1+ 0.06136/12 )^-48

=9418.98 is the original monthly payments

Now she wants to pay twice the regular payments =

New payment = 2*9418.98 = 18,837.95

So

Substituting the value in the equation

Monthly payment = P*(i/m)   / ( 1- (1+i/m) –mt

18,837.95= 400000 * (0.06136/12) / 1-(1+ 0.06136/12 )^-t

We get

Time = 22.6 months Option B answer