Suppose you borrowed $15,000 at a rate of 9% and must repay it in 5 equal installments at the end of each of the next 5 years. What is the outstanding balance of the loan at the end of second year?
First find the payment using:
Present Value = payment (1 - (1+i)^-n)/i
where i is the rate expressed as a decimal , i = .09, and n is the number of interest periods. n = 5
outstanding balance after 2 years
= 15000(1.09)^2 - payment( 1.09^2 - 1)/.09
let me know what you get
To find the outstanding balance of the loan at the end of the second year, we need to calculate the remaining balance after the first two installments.
First, let's calculate the annual repayment amount. Since you borrowed $15,000 and need to repay it in 5 equal installments, each installment will be $15,000 divided by 5, which equals $3,000.
Next, let's calculate the interest for the first year. The interest rate is 9%, so the interest for the first year will be 9% of the initial loan amount, which is $15,000. Therefore, the interest for the first year is $15,000 multiplied by 9% (or 0.09), which equals $1,350.
Now, subtract the interest for the first year from the first installment to find out how much of the payment goes towards reducing the loan amount. The first installment is $3,000, so the amount that goes towards the loan principal is $3,000 minus $1,350, which equals $1,650.
After the first year, the remaining balance on the loan will be the initial loan amount minus the amount paid towards the loan principal. So the remaining balance after the first year is $15,000 minus $1,650, which equals $13,350.
Now, let's repeat the calculation for the second year. The interest for the second year is 9% of the remaining balance after the first year, which is $13,350. Thus, the interest for the second year is $13,350 multiplied by 9% (or 0.09), which equals $1,201.50.
Subtract the interest for the second year from the second installment to find out how much of the payment goes towards reducing the loan amount. The second installment is $3,000, so the amount that goes towards the loan principal is $3,000 minus $1,201.50, which equals $1,798.50.
Finally, calculate the remaining balance after the second year by subtracting the amount paid towards the loan principal in the second year from the remaining balance after the first year. The remaining balance after the second year is $13,350 minus $1,798.50, which equals $11,551.50.
Therefore, the outstanding balance of the loan at the end of the second year is $11,551.50.