After 12 months of making extra payments, what will be the loan balance? After 12 months of making the regular
payment and investing the $50, what will be the loan balance?
Under the regular payment and investing option, excluding the tax due on the interest earned, what is the investment balance after 12 months? Compare the scenarios of investment versus prepayment by examining the 60th payment, which occurs at the end of the fifth year. What is the difference between the (a) interest portion of that payment, (b) tax deduction for interest, and (c) principal balance? Finally, how much is in the investment account? (a) How long does it take to repay the entire loan under the prepayment option? (b) What is the total interest paid over the life of the loan? Compare the total interest paid under each scenario? How much less in interest do you pay under the prepayment option?
Loan Balance: $135000
Current Payment: $990.62
Additional Payment: $50.00
Loan Interest Rate: 8.0%
Loan Interest Deductibility: YES
Investment Rate Return: 6.00%*
Tax Bracket: 30.00%
Investment Type: After-Tax
An EXCEL spreadsheet is very helpful for these types of problems. Just set it up. eg., the balance formula (no extra payments) is: B1 = (B0-P)*(1+.08/12)
To calculate the loan balance after 12 months of making extra payments, you will need to know the loan balance, payment amount, additional payment, and the interest rate. Let's assume the loan balance is $135,000, the current payment is $990.62, and the additional payment is $50. The loan interest rate is 8.0%.
To calculate the loan balance after 12 months of making extra payments, you can follow these steps:
1. Calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 8.0% / 12 = 0.0067.
2. Calculate the interest for the first month by multiplying the loan balance by the monthly interest rate. The interest for the first month is $135,000 * 0.0067 = $904.50.
3. Subtract the interest for the first month from the total combined payment (current payment + additional payment) to get the principal paid for the first month. In this case, the principal paid for the first month is $1,040.82 - $904.50 = $136.32.
4. Subtract the principal paid for the first month from the loan balance to get the loan balance after the first month. In this case, the loan balance after the first month is $135,000 - $136.32 = $134,863.68.
5. Repeat steps 2-4 for the remaining 11 months, using the updated loan balance each month.
After 12 months of making the regular payment and investing the extra $50, you will need to calculate the investment balance. To do this, you will need to know the investment rate of return, the tax bracket, and the investment type (after-tax).
Let's assume the investment rate of return is 6.00%, the tax bracket is 30.00%, and the investment type is after-tax.
To calculate the investment balance after 12 months, you can follow these steps:
1. Calculate the after-tax rate of return by multiplying the investment rate of return by (1 - (tax bracket / 100)). In this case, the after-tax rate of return is 6.00% * (1 - (30.00% / 100)) = 4.20%.
2. Multiply the additional payment by the after-tax rate of return to get the investment return for the first month. In this case, the investment return for the first month is $50 * 0.042 = $2.10.
3. Add the investment return for the first month to the investment balance from the previous month to get the investment balance after the first month. If this is the first month, then the investment balance will be the investment return for the first month. In this case, the investment balance after the first month is $2.10.
4. Repeat steps 2-3 for the remaining 11 months, using the updated investment balance each month.
To compare the scenarios of investment versus prepayment by examining the 60th payment, which occurs at the end of the fifth year, you will need to calculate the difference in the interest portion of the payment, tax deduction for interest, principal balance, and the investment account balance.
To calculate the difference in the interest portion of the 60th payment between the scenarios, you can follow these steps:
1. Calculate the principal balance after 60 payments for both scenarios. To do this, subtract the sum of the principal paid for each payment in the first 60 months from the initial loan balance. Keep in mind that with prepayment, the additional payment can be applied to principal, whereas in the regular payment and investing scenario, the additional payment is invested.
To calculate the tax deduction for interest, you will need to know if the loan interest is tax-deductible and the tax bracket. In this case, the loan interest is tax-deductible and the tax bracket is 30.00%.
To calculate the tax deduction for interest, you can follow these steps:
1. Multiply the interest portion of the payment by the tax bracket as a decimal (e.g., 30.00% as 0.30) to get the tax deduction for interest.
To calculate the investment account balance after the 60th payment, you will need to calculate the investment return for each month and add it to the previous investment balance.
To calculate how long it takes to repay the entire loan under the prepayment option, you will need to determine the number of payments required. By dividing the initial loan balance by the combined payment amount, you can calculate the number of months or years it takes to repay the loan.
To calculate the total interest paid over the life of the loan, you will need to calculate the sum of the interest paid for each payment.
To compare the total interest paid under each scenario, subtract the total interest paid under the prepayment option from the total interest paid under the regular payment and investing option.
To calculate how much less interest you pay under the prepayment option, subtract the total interest paid under the prepayment option from the total interest paid under the regular payment and investing option.