A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid under the following two options. Equal annual payments at an annual effective rate of 8.07%. Installments of 200 each year plus interest on the unpaid balance at an annual effective rate of i The sum of the payments under option (i) equals the sum of payments under option (ii). Calculate i.

Question

Mathematics

Ainsley Thompson

18 April, 22:13

A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid under the following two options. Equal annual payments at an annual effective rate of 8.07%. Installments of 200 each year plus interest on the unpaid balance at an annual effective rate of i The sum of the payments under option (i) equals the sum of payments under option (ii). Calculate i.

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Answers (2)

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Joshua · Answer 1

Answer: i=9%

Step-by-step explanation:

2000 = x/1.0807 + x/1.0807^2 ... + x/1.0807^10

2000 = x (6.6889)

x = $299 per month

Given that the payment under each option is the same:

299*10 = 200 * 10 + I

I (Total Interest paid) = $990

I = (2000 * i) + (1800 * i) + (1600 * i) + ...

$990 = i (2000 + 1800 + ... + 200)

$990 = i * 11000

i = 9%

Elliot Schultz · Answer 2

The answer to the question is i = 9%

Step-by-step explanation:

From the example given, let recall the following formula,

10 year loan of = 2000

The equal annual payments at an annual effective rate = 8.07%

The installment for each year = 200

Them

2000 = x/1.0807 + x/1.0807^2 + ... x/1.0807^10

2000 = x (6.6889)

x = $299 per month

The payment under under each option is the same:

299*10 = 200 * 10 + I

I (Total Interest paid) = $990

I = (2000 * i) + (1800 * i) + (1600 * i) +

$990 = i (2000 + 1800 + ... + 200)

$990 = i * 11000

Therefore i = 9%