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.

Solutions

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 1 year ago

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