Josh borrows some money on which he makes monthly payments of $125.43 for 3 years. If the interest rate is 5.4%/a compounded monthly, what will be the total amount of all of the payments at the end of the 3 years?
To find the total amount of all the payments at the end of 3 years, we need to calculate the total repayment including both the principal amount borrowed and the interest accrued.
First, we need to determine the principal amount borrowed. We know that Josh makes monthly payments of $125.43 for 3 years, so we can calculate the total number of payments made over the 3-year period:
Total number of payments = 12 months/year * 3 years
Total number of payments = 36 payments
Next, we can use the formula for the present value of an annuity to find the principal amount borrowed:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value (principal amount borrowed)
PMT = Monthly payment
r = Monthly interest rate (expressed as a decimal)
n = Total number of payments
Let's calculate the principal amount borrowed:
PV = $125.43 * [(1 - (1 + 0.054/12)^(-36)) / (0.054/12)]
PV ≈ $4114.51 (rounded to the nearest cent)
Now that we have the principal amount borrowed, we can calculate the total amount of all the payments:
Total amount of payments = Monthly payment * Total number of payments
Total amount of payments = $125.43 * 36
Total amount of payments ≈ $4515.48 (rounded to the nearest cent)
Therefore, the total amount of all the payments made at the end of the 3-year period will be approximately $4515.48.