Question

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
6^{th} payment.

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

Answer #1

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 |
|||||

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 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.
Please solve by hand, I need to know how to complete the problem
without a financial calculator. Thank you.

A loan is being repaid by quarterly installments of $1500 at the
end of each quarter at 10% convertible quarterly. If the loan
balance at the end of the first year is $12,000. Find the original
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end of each quarter at 10% convertible quarterly. If the loan
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calculate the outstanding loan balance at the end of the first
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Show working please, should not be done in excel. THANK
YOU.

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