Jo’s monthly repayment on a loan at 13% p.a.
over 3 years is $808.56. How much did Jo
borrow?

To determine how much Jo borrowed, we can use the formula for calculating the present value of an annuity, which is typically used for loan repayments:

\[
PV = \frac{R \times (1 - (1 + r)^{-n})}{r}
\]

Where:
- $ PV $ is the present value or the loan amount (which is what we're trying to find).
- $ R $ is the monthly repayment amount, which is $808.56.
- $ r $ is the monthly interest rate (annual interest rate divided by 12).
- $ n $ is the total number of payments (number of years multiplied by 12).

Given:
- Annual interest rate = 13% = 0.13 (as a decimal).
- Monthly interest rate $ r = \frac{0.13}{12} $.
- Number of years = 3.
- Total number of payments $ n = 3 \times 12 = 36 $ months.

Now we can plug in the values:

\[
PV = \frac{808.56 \times \left(1 - (1 + \frac{0.13}{12})^{-36}\right)}{\frac{0.13}{12}}
\]

Let's calculate this.Jo borrowed approximately **$23,997.19**.

Would you like any more details or have any questions?

Here are some related questions you might find interesting:

1. What is the total amount Jo will repay over the 3 years?
2. How would the monthly payment change if the loan term was 5 years instead of 3?
3. What would be the loan amount if the interest rate was 10% instead of 13%?
4. How does compound interest affect the loan repayment amount?
5. What is the impact of making additional payments on the loan?
6. How much interest will Jo pay over the life of the loan?
7. How does the loan amount change with different repayment frequencies (e.g., bi-weekly)?
8. How would the loan amount change if the monthly payment was $900 instead of $808.56?

**Tip:** Always consider the total interest paid over the loan's lifetime when deciding on loan terms.

Discover how to calculate the loan amount Jo borrowed with a 13% annual interest rate over 3 years using the present value of annuity formula. Jo's monthly repayment is $808.56. Get a detailed explanation and step-by-step calculation.

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