Question

A loan of $10000 is being repaid with level payments at the end of each year for 10years. Assuming 10% effective interstate's per year, the borrower pays an extra x dollars with their 5th payment which allows the same level payments to exactly pay off the loan two years earlier. Find X

Answer #1

The loan repayment is a normal annuity , the present value of which equals loan amount. The level payment (A) is calculated as

A* Present value annuity factor = 10000

=> A * (1-1/1.1^10)/0.1 = 10000

=> 6.14457*A =10000

=> A= **$1627.45**

Now, the present value of 8 payments of $1627.45 + present value of $X at the end of 5th year should also be equal to loan amount

1627.45/0.1*(1-1/1.1^8)+X/1.1^5 = 10000

=> 8682.35 + X/1.1^5 = 10000

=> X/1.1^5 =1317.653

=> X =2122.09

So, the amount X has to be equal to
**$2122.09**

A 25-year loan is being repaid with annual payments of 1,300 at
an annual effective rate of interest of 7%. The borrower pays an
additional 2,600 at the time of the 5th payment and wants to repay
the remaining balance over 15 years.
Calculate the revised annual payment.

A 20-year loan is to be repaid with level payments at the end of
each year. The amount of interest paid in the 5th payment is
103.17. The amount of interest paid in the 13th payment is 57. Find
the amount of interest and principal paid in the 17th payment.
(Answers: 30, 270.)

A loan of $10,000 is being repaid with 10 payments at the end of
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calculations.

A 10 year loan is being repaid with payments at the end of each
year in the following manner. The first payment is $5,000 and each
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borrowed. Assume i(4) = 6%.

A loan of $6,300 is being repaid by payments of $70 at the end
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calculate the outstanding loan balance at the end of the first
year.

A loan of 20,000 is being repaid by 20 annual payments at the
end of year, each includes equal repayment of the principal along
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each year for 10
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each, with there being 20 end of quarter payments total. The
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Please show/explain your work, I'd like to learn how to do it
without excel

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.

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