You are planning to borrow OMR 5,000. You can repay the loan in 40 monthly payments of OMR 147.50 each or 36 monthly payments of OMR 161.34 each. You decide to take the 40-month loan. During each of the first 36 months you make the loan payment and place the difference between the two payments (OMR 13.84) into an investment account earning 10% APR. Beginning with the 37th payment you will withdraw money from the investment account to make your payments. How much money will remain in the investment account after your loan is repaid?
Here is a hint:
Take 10% of an investment, that should be a good first step.
To calculate the amount of money that will remain in the investment account after your loan is repaid, we need to follow these steps:
Step 1: Calculate the total amount repaid over the duration of the loan.
The monthly payment amount for the 40-month loan is OMR 147.50. Therefore, the total amount repaid over the 40 months is:
Total amount repaid = Monthly payment amount * Number of months
= OMR 147.50 * 40
= OMR 5,900
Step 2: Calculate the total amount saved by investing the difference between the two payment options.
The difference between the two monthly payments is OMR 13.84. You invest this amount every month for the first 36 months. The investment account earns an annual interest rate of 10%.
First, we calculate the monthly interest rate:
Monthly interest rate = Annual interest rate / 12
= 10% / 12
= 0.833%
Next, we calculate the future value of the monthly investments after 36 months:
Future value = Monthly investment amount * (((1 + Monthly interest rate)^Number of months) - 1) / Monthly interest rate
= OMR 13.84 * (((1 + 0.00833)^36) - 1) / 0.00833
≈ OMR 684.51
Step 3: Calculate the remaining balance in the investment account after the loan is repaid.
Starting from the 37th payment, you will withdraw money from the investment account to make the monthly loan payments. To calculate the remaining balance, we need to subtract the monthly withdrawals from the investment account.
Remaining balance = Future value - (36 months * (OMR 161.34 - OMR 147.50))
= OMR 684.51 - (36 * OMR 13.84)
= OMR 684.51 - OMR 498.24
= OMR 186.27
Therefore, after your loan is repaid, approximately OMR 186.27 will remain in the investment account.