Bryan decides to purcahse a new car with a price of 14000 dollars ,but cannot afford the full amount .The car dealers offers him options to finance loan .A 6 year loan to annual interest of 14% compounded quarterly .No deposit and repayments are made each quater .Find the repayment made each quarter


To find the repayment Bryan must make each quarter, we can use the formula for the present value of an annuity. This formula applies since Bryan is paying off a loan with equal payments (repayments) made regularly (each quarter) over a set period of time, with interest compounded periodically (quarterly).

The formula for the quarterly payment $ R $ is:

\[
R = \frac{P \cdot i}{1 - (1 + i)^{-n}}
\]

Where:
- $ P $ is the loan amount (the principal) = 14,000 dollars
- $ i $ is the interest rate per period = $\frac{14\%}{4}$ per quarter = $ \frac{0.14}{4} = 0.035 $
- $ n $ is the total number of payments = 6 years $\times$ 4 quarters per year = 24 quarters

Let’s calculate the quarterly repayment amount.The quarterly repayment Bryan needs to make is approximately \$871.82.

Would you like further details on how this was calculated, or any other questions? Here are 5 related questions you might be interested in:

1. How is interest compounded in loans, and why does it affect repayments?
2. What would happen if the interest were compounded monthly instead of quarterly?
3. How would changing the loan term affect the quarterly payment?
4. What is the total amount Bryan will pay over the 6 years?
5. How does an amortization schedule work for this type of loan?

**Tip:** Always make sure to compare different loan options, including how often interest is compounded, as it significantly affects total repayment amounts.

Bryan decides to purchase a new car with a price of 14000 dollars, but cannot afford the full amount. The car dealer offers him options to finance a loan: a 6-year loan with an annual interest of 14% compounded quarterly. No deposit and repayments are made each quarter. Find the repayment made each quarter.

Calculate the quarterly repayments for a 6-year car loan of $14,000 with 14% annual interest compounded quarterly. Learn how to use the present value of an annuity formula to determine the quarterly payment amount of approximately $871.82. Suitable for high school students learning financial mathematics.

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