SOLUTION: A man takes out a $20 000 bank loan that accrues 8% interest each year. A man decides to pay off only the interest each year, and deposit a different amount X into an interest acco

Question 1166131: A man takes out a $20 000 bank loan that accrues 8% interest each year. A man decides to pay off only the interest each year, and deposit a different amount X into an interest account that earns him 4% interest each year.
a) If the man decides to pay off the loan in 10 years how much does he spend on interest alone?
b) How much should he deposit into the interest account each year so that at the end of 10 years he can pay back the initial $20 000?
c) How much has the man spent totally?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the payments on the loan are 2,980.59 at the end of each year for 10 years.

that makes the total amount he spent on the loan equal to 29,805.9.

the sum of the interest part of the total payments that he made is equal to 29,805.9 minus 20,000 = 9,805.9.

the payments on the investment account are 1,665.82 at the end of each year for 10 years.

that makes the total amount he spent on the investment account equal to 16,658.2.

his total payments for the 10 years equals 29,805.9 + 16,658.2 = 46,464.1.

29,805.9 of that is the total payments made to pay off the 20,000 loan at the start of the investment period.

16,658.2 of that is the total payments made to receive 20,000 at the end of the investment period.

the total interest that he paid in order to pay off the 20,000 loan at the beginning of the investment period was 29,805.2 minus 20,000 = 9,805.2

the total interest that he earned by investing to receive 20,000 at the end of the investment period was 20,000 minus 16,658.2 = 3,341.8.

the answers to your questions are shown below:

a) If the man decides to pay off the loan in 10 years how much does he spend on interest alone?

he spent 9,805.2 on interest alone.

b) How much should he deposit into the interest account each year so that at the end of 10 years he can pay back the initial $20,000?

he needed to deposit 1,665.82 each year.

c) How much has the man spent totally?

the total he spent to satisfy the loan of 20,000 at the beginning of the investment period was 29805.9.
the total he spent to earn 20,000 at the end of the investment period was 16658.2

the total he spent was therefore 29,805.9 plus 16,658.2 = 46,464.1

here's a display of the calculator results for paying off the 20,000 loan at the start of the investment period.

here's a display of the calculator results for investing to receive 20,000 at the end of the investment period.

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