A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year. It can be repaid under the

Question

A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year. It can be repaid under the following two options: i. Equal annual payments at an annual effective rate of 5.50%. ii. Installments of $300 each year plus interest on the unpaid balance at an annual effective rate of i. The sum of the payments under option (i) equals the sum of the payments under option (ii). Find i.

Help In Homework · Accepted Answer

loan amount 3000 option 1 equal anuual payments interst rate 5.50% EAI = P × r × (1 + r)n/((1 + r)n - 1) where P= Loan amount, r= interest rate, n=tenure in number of years 3000*0.055*(1+0.055)^10/((1+0.055)^10-1) 398.0033061 total amount paid 3980.03306 Option 2 year opening amt principle paid interest 1 3000 300 3000*i 2 2700 300 2700*i 3 2400 300 2400*i 4 2100 300 2100*i 5 1800 300 1800*i 6 1500 300 1500*i 7 1200 300 1200*i 8 900 300 900*i 9 600 300 600*i 10 300 300 300*i Total 3000 16500*i total in option 1 and option 2 are same 3980=3000+16500*i 16500*i=980 i=980/16500 i= 0.059393939 i.e. 5.9393 5.94%

Why Choose Us?

0% AI Guarantee

24/7 Support

Plagiarism Free

Expert Tutors

100% Confidential

On-Time Delivery

A 10-year loan of $3,000 is arranged to be settled by payments at the end of each year

Expert Solution

Archived Solution

	loan amount	3000

	option 1	equal anuual payments
	interst rate	5.50%

	EAI = P × r × (1 + r)n/((1 + r)n - 1) where P= Loan amount, r= interest rate, n=tenure in number of years
	30000.055(1+0.055)^10/((1+0.055)^10-1)
	398.0033061
	total amount paid	3980.03306

	Option 2

year	opening amt	principle paid	interest
1	3000	300	3000*i
2	2700	300	2700*i
3	2400	300	2400*i
4	2100	300	2100*i
5	1800	300	1800*i
6	1500	300	1500*i
7	1200	300	1200*i
8	900	300	900*i
9	600	300	600*i
10	300	300	300*i
	Total	3000	16500*i

	total in option 1 and option 2 are same
	3980=3000+16500*i
	16500*i=980
	i=980/16500
i=	0.059393939
	i.e. 5.9393
	5.94%