Question

Harris Machinery received a demand loan of $180,000. It repaid $70,000 at the end of the first year, $90,000 at the end of the second year, and the balance at the end of the third year. The interest rate charged on the loan was 5.75% compounded semi-annually during the first year, 5.50% compounded quarterly during the second year, and 4.75% compounded monthly during the third year.

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

Round to the nearest cent

b. What was the balance of the loan at the end of the second year?

Round to the nearest cent

c. What amount at the end of the third year will settle the loan?

Answer 1

a. Balance of the loan at the end of the first year = $ 120498.78

b. Balance of the loan at the end of the second year = $ 37264.16

c. Amount at the end of the third year will settle the loan = $ 39073.26

Year	Interest Amount	Calculation of Interest	Total (Opening Bal + Interest)	Payment (given)	BALANCE (Total - Payment)	RATE (given)
					180000.00
1	10498.78	=Loan Amount*((1+(RATE/2))^2-1)	190498.78	70000.00	120498.78	5.75%
2	6765.38	=Previous Balance*((1+(RATE/4))^4-1)	127264.16	90000.00	37264.16	5.50%
3	1809.10	=Previous Balance*((1+(RATE/12))^12-1)	39073.26	39073.26	0.00	4.75%

Interest Calculation Details:

Year	Interest Amount	Calculations
1	10498.78	=180000*((1+(0.0575/2))^2-1)
2	6765.38	=120498.78*((1+(0.055/4))^4-1)
3	1809.10	=37264.16*((1+(0.0475/12))^12-1)

Formula used for Interest is as below:

[Where,

I = Interest amount for the year

R = Rate of Interest p.a.

n = Number of Compounding per year OR Number of compounding per period

t =Number of Years ]

*In all the above cases number of years is ONE as each year has different rate and different compounding.