Question

Mr. Bronson wants to be one of the investors in the new Sergio Leone movie called The Good, The Bad and The Ugly. He needs to borrow $1580000 from a bank at an interest rate of 6.9% compounded quarterly to invest in this movie. The loan will be repaid in 27 equal monthly payments. His first payment will be made one month after the day he borrows the money (i.e. at the end of month one). (round your final answers to 4 decimal point)

a) What is the amount of his monthly payments?

b) What are the interest and principal payments in his 7th monthly payment. (round your final answers to 1 decimal point)

Answer 1

a.
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+(6.9%/4)^4)-1)
Effective annual rate	1.070806-1
Effective annual rate	7.08%
Monthly interest rate	0.0059005	7.08%/12
No of payments	27
Formula to calculate monthly payment
Monthly payment	Loan amount/Annuity discount factor
Annuity discount factor	[1-((1+r)^-n)]/r
interest rate is r and number of payments is n
Monthly payment	1580000/(1-(1.0059^-27))/0.0059
Monthly payment	1580000/24.8914
Monthly payment	$63,475.7431
b.
We would prepare amortization table for 7 months to determine interest and principal paid
Time	Annual payment	Interest	Principal	Loan balance
				$1,580,000.0
1	$63,475.7	$9,322.8	$54,153.0	$1,525,847.0
2	$63,475.7	$9,003.3	$54,472.5	$1,471,374.6
3	$63,475.7	$8,681.8	$54,793.9	$1,416,580.7
4	$63,475.7	$8,358.5	$55,117.2	$1,361,463.5
5	$63,475.7	$8,033.3	$55,442.4	$1,306,021.0
6	$63,475.7	$7,706.2	$55,769.6	$1,250,251.5
7	$63,475.7	$7,377.1	$56,098.6	$1,194,152.8
The 7th payment would have interest of $7,377.1 and principal payment of $56,098.6
Interest	Beginning loan balance*0.0059
Principal	Annual payment - Interest expense