Question

A design studio received a loan of $5,300 at 3.10% compounded semi-annually to purchase a camera. If they settled the loan in 2 years by making quarterly payments, construct the amortization schedule for the loan and answer the following questions:

a. What was the payment size?

Round to the nearest cent

b. What was the size of the interest portion on the first payment?

Round to the nearest cent

c. What was the balance of the loan at end of the first year?

Round to the nearest cent

d. What was the size of the interest portion on the last payment?

Round to the nearest cent

Answer 1

In this case we will have to calculate annual effective interest rate and then calculate monthly payment
Effective annual rate	(1+(r/n)^n)-1)
interest rate is r and frequency of compounding is n
Effective annual rate	(1+(3.10%/2)^2)-1)
Effective annual rate	1.03124-1
Effective annual rate	3.12%
Quarterly interest rate	0.00781	3.12%/4
No of payments	8	2*4
Formula to calculate quarterly payment
Quarterly payment	Loan amount/Annuity discount factor
Annuity discount factor	[1-((1+r)^-n)]/r
interest rate is r and number of payments is n
Quarterly payment	5300/(1-(1.00781^-8))/0.00781
Quarterly payment	5300/7.726003
Quarterly payment	$686.00
Amortization table
Time period	Quarterly payment	Interest	Principal payment	Loan balance
1	$686.00	$41.39	$644.60	$4,655.40
2	$686.00	$36.36	$649.64	$4,005.76
3	$686.00	$31.29	$654.71	$3,351.05
4	$686.00	$26.17	$659.82	$2,691.23
5	$686.00	$21.02	$664.98	$2,026.25
6	$686.00	$15.83	$670.17	$1,356.08
7	$686.00	$10.59	$675.40	$680.68
8	$686.00	$5.32	$680.68	$0.00
Interest is calculated as beginning loan balance*Quarterly interest rate (0.00781)
Principal payment	Quarterly payment - Interest for the period
b.
The interest portion in first payment was $41.39
c.
Balance of loan at end of year 1 is $2,691.23 (after 4th payment)
d.
The interest portion in last payment is $5.32