If you buy a computer directly from the manufacturer for $ 2 comma 628 and agree to repay it in 48 equal installments at 1.78 % interest per month on the unpaid balance, how much are your monthly payments?
The correct answer and explanation is:
To find the monthly payment on a loan, we use the installment loan formula: P=r⋅PV1−(1+r)−nP = \dfrac{r \cdot PV}{1 – (1 + r)^{-n}}
Where:
- PP is the monthly payment
- PVPV is the present value or loan amount ($2,628)
- rr is the monthly interest rate (1.78% = 0.0178)
- nn is the number of monthly payments (48)
Step-by-step Calculation:
P=0.0178×26281−(1+0.0178)−48P = \dfrac{0.0178 \times 2628}{1 – (1 + 0.0178)^{-48}}
- Multiply interest rate by the loan amount:
0.0178×2628=46.77840.0178 \times 2628 = 46.7784
- Calculate the denominator:
(1+0.0178)−48=(1.0178)−48≈0.423(1 + 0.0178)^{-48} = (1.0178)^{-48} \approx 0.423 1−0.423=0.5771 – 0.423 = 0.577
- Divide:
P=46.77840.577≈81.06P = \dfrac{46.7784}{0.577} \approx 81.06
Final Answer:
Your monthly payments will be approximately $81.06
Explanation:
When purchasing a product on credit with monthly installments and interest, the lender charges you for borrowing the money. This cost is spread over equal payments for a certain period. In this case, you’re borrowing $2,628 and agreeing to pay it back over 48 months (4 years) with 1.78% monthly interest.
The formula used is based on the mathematics of amortizing loans, where part of each monthly payment goes to interest, and the rest reduces the principal. Early in the repayment period, more of your payment goes toward interest, but as the loan progresses, more goes toward the principal.
Using this formula ensures that each monthly payment remains the same, making budgeting easier. Even though interest accumulates monthly, the loan is designed so you know exactly what you’ll pay each month, in this case, around $81.06.