A loan is to be repaid by twenty end of quarter payments of $1,000. The interest...

A loan is to be repaid by twenty end of quarter payments of $1,000. The interest rate for the first two years is 6% convertible quarterly, and last three years is 8% convertible quarterly. Find the outstanding loan balance just after the 5^th payment.

Please don't use Excel! I'm looking to learn how to do it with the formulas.

Expert Solution

In this case we will have to calculate present value of the remaining payments pending afer 5th payment

Quarterly interest rate for first two years	1.50%	6%/4
Quarterly interest rate for last three years	2.00%	8%/4

Present value	Annual payment*(1-((1+r)^-n))/r
Interest rate is r and number of payment is n

No of payments for first two years	8	(2*4)
Remaining payments after 5th payment	3	(8-5)
No of payments of last three years	12	3*4
The interest rate are different and thus present value calculation is spilt

Loan outstanding after 5th payment	1000(1-(1.015^-3))/0.015)+1000(1-(1.02^-12)/0.02)
Loan outstanding after 5th payment	10002.9122+100010.57534
Loan outstanding after 5th payment	$13,487.54

Thus, remaining loan balance after 5th payment is $13,487.54

jeff jeffy answered 2 years ago

A loan is to be repaid in end of quarter payments of $1,000 each, with there...

A loan is to be repaid in end of quarter payments of $1,000 each, with there being 20 end of quarter payments total. The interest rate for the first two years is 6% convertible quarterly, and the interest rate for the last three years is 8% convertible quarterly. Find the outstanding loan balance right after the 6th payment.

A loan is being repaid with 20 payments of $ 1,000 at the end of each...

A loan is being repaid with 20 payments of $ 1,000 at the end of each quarter. Given that the nominal rate of interest is 8% per year compounded quarterly, find the outstanding balance of the loan immediately after 10 payments have been made (a) by the prospective method, (b) by the retrospective method.

A 30-year loan of 1,000 is repaid with payments at the end of each year. Each...

A 30-year loan of 1,000 is repaid with payments at the end of each year. Each of the first ten payments equals the amount of interest due. Each of the next ten payments equals 150% of the amount of interst due. Each of the last ten payments is X. The lender charges interest at an annual effective rate of 10%. Calculate X.

A loan of 10000$ is to be repaid with annual payments, at the end of each...

A loan of 10000$ is to be repaid with annual payments, at the end of each year, for the next 20 years. For the rst 5 years the payments are k per year ; the second 5 years, 2k per year ; the third 5 years, 3k per year ; and the fourth 5 years, 4k per year. (a) Draw two timelines describing this series of payments. (b) For each of the timelines in (a), find an expression for k...

A 10-year loan of 120,000 is to be repaid with payments at the end of each...

A 10-year loan of 120,000 is to be repaid with payments at the end of each month. Interest is at an annual effective rate of 6.00%. The first monthly payment is 800. Each additional payment will be k more than the previous month payment. Find k.

A loan of $5000 is repaid with annual payments at the end of each year of...

A loan of $5000 is repaid with annual payments at the end of each year of $1200,$800,$1300 and X. Assume the loan has 10% effective interest per year. a) Determine X b) Determine the amount of interest paid with the third payment.

A loan of $12,000 is repaid by payments of $571 at the end of every three...

A loan of $12,000 is repaid by payments of $571 at the end of every three months. Interest is 9% compounded quarterly (a) How many payments are required to repay the debt? (b) What is the size of the final payment?

A loan of $12,000 is being repaid with payments of $1,500 at the end of each...

A loan of $12,000 is being repaid with payments of $1,500 at the end of each year for 10 years. These payments can earn interest at an effective rate of 6% per annum. At the end of the year, this interest is reinvested at the annual effective rate 5% for the first 6 years and only 4% for the second 4 years. Find the yield rate over the 10-year period.

Donald takes out a loan to be repaid with annual payments of $500 at the end...

Donald takes out a loan to be repaid with annual payments of $500 at the end of each year for 2n years. The annual effective interest rate is 4.94%. The sum of the interest paid in year 1 plus the interest paid in year n + 1 is equal to $720. Calculate the amount of interest paid in year 10.

a 30 year loan of 1000 is repaid with payments at the end of each year....

a 30 year loan of 1000 is repaid with payments at the end of each year. Each of the first 10 payments equals the amount of interest due. Each of the next 10 payments equals 150% of the amount of interest due. Each of the last 10 payments is X. The lender charges interest at an effective annual rate of 10%. Calculate X. please explain, having much trouble with this problem, Thanks!

Question