Question

1. The owner of a hotel borrowed $13 000 at 7.8% compounded semi-annually and agreed to repay the loan by making payments of $750 at the end of every 4 months.
   1. How much payments will be needed to repay the loan?
   2. How much will be owed at the end of 5 years?
   3. By the end of 5 years of payments, what is the total interest payed?

2. A contract valued at $28 000 requires payments of $6500 every 6 months. The first payment is due in 5 years and interest is 12% compounded semi-annually.
   1. How many payments are required?
   2. What is the size of the last payment?

Answer 1

Given

Loan amount = $13000

Rate of interest = 7.8%

Compounding (m) = 2

Payment=$750

a)

Number of times repaid in a year (n) = 3

Effective annual rate of interest = ((1+APR/m)^m/n)-1

                                                                =((1+7.8%/2)^2/3)-1

                                                                = 2.583%

Now

Using Excel we can calculate number payment needed to repay the loan

Number of payments = NPER(rate,pmt,pv,fv)

                                                = NPER(2.583%,-750,13000,0)

                                                = 23payments

b)

No of payments in 5 years = 3*5 = 15

Using Excel:

PV=PV(rate,NPeR,-pmt,fv)

   =PV (2.583%,15,-750,0)

   = $9229.59

c)

Total installments paid =750*15 = 11250

Loan amount paid off in 5 years = 13000-9229.59 = 3770.41

Interest paid = 11250-3770.41 = $7479.59

Please post 2 question seperately. Thank you