Question

# 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.

Please show/explain your work, I'd like to learn how to do it without excel

 In this case we will have to calculate present value of the remaining payments pending afer 6th 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 6th payment 2 (8-6) 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 6th payment 1000*(1-(1.015^-2))/0.015)+1000*(1-(1.02^-12)/0.02) Loan outstanding after 6th payment 1000*1.9559+1000*10.57534 Loan outstanding after 6th payment \$12,531.22 Thus, remaining loan balance after 6th payment is \$12,531.22

#### Earn Coins

Coins can be redeemed for fabulous gifts.