Question

Kevin takes out a 10-year loan of L, which he repays by the amortization method at an annual effective interest rate of i. Kevin makes payments of 1000 at the end of each year. The total amount of interest repaid during the life of the loan is also equal to L. Calculate the amount of interest repaid during the first year of the loan.

Answer 1

Answer:

first year interest paid: 754.92 dollars

Explanation:

Kevin makes 10 payment of 1,000 dollars

This pays interest and principal

we know that principal is L and total interest is also L

so: principal = total interest

10,000 = principal + total interest

10,000 = 2L

L = 5,000

the principal is 5,000 and the interest are 5,000

To know the interest in the first period we need to solve for rate of a 10 years annuity of 1,000:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

$1000 \times \frac{1-(1+r)^{-10} }{r} = 5,000$

This is solve with financial calculator or excel using "goal seek" in the Data pannel.

This will give us: 0.150984145

Now, we calcualte the interest for the first year:

principal x rate

5,000 x 0.150984145 = 754.920726 = 754.92 dolllars