Question

A construction company signed a loan contract at 4.62​% compounded semi-annually​, with the provision to pay ​$725 at the end of each month for three years.

​(a) What is amount of the​ loan?

​(b) How much will be owed at the end of sixteen ​months?

​(c) How much of the principal will be repaid within the first sixteen ​months?

​(d) How much interest is paid during the first sixteen ​months?

Answer 1

Monthly payment =725

total number of monthly payment (n) =3*12 =36

semiannual rate = 4.62%/2 =0.0231

Effective semiannual rate = ((1+monthly rate or i)^number of months in semiannual period)-1

0.0231 = ((1+i)^6)-1

1+0.0231=(1+i)^6

(1+i) = (1.0231)^(1/6)

i = 1.003813458-1

=0.003813458

So monthly rate i is 0.003813458

Loan value formula = monthly payment*(1-(1/(1+i)^n))/i

=725*(1-(1/(1+0.003813458)^36))/0.003813458

=24344.40626

So loan amoun t is 24344.41

b.

Monthly payment =725

number of months remaining to pay (n) =36-16 = 20

monthly rate i is 0.003813458

Loan balance formula = monthly payment*(1-(1/(1+i)^n))/i

=725*(1-(1/(1+0.003813458)^20))/0.003813458

=13935.28807

So balance owed after 16 months is $13935.29

c

Principal repaid = loan amount - loan balance at 16 months

=24344.40626-13935.28807

=10409.11819

So Principal repaid in 16 months is $10409.12

d.

interet repaid in 16 months = (monthly payment * number of months)-principal repaid in 16 months

=(725*16)-10409.11819

=1190.88181

So interest repaid is $1190.88