Niamh has saved to buy a car - Leaving Cert Mathematics - Question 4 - 2013

The future value of the savings can be calculated using the formula for the future value of an annuity:

$P = A \times \frac{(1 + i)^n - 1}{i}$

Where:

• $P$ is the future value (€15,000)
• $A$ is the monthly savings amount
• $i$ is the monthly interest rate (0.003273)
• $n$ is the number of months (36)

Rearranging for $A$ gives us:

$A = P \times \frac{i}{(1 + i)^n - 1}$

Substituting the values:

$A \approx 15000 \times \frac{0.003273}{(1 + 0.003273)^{36} - 1}$

Calculating this yields:

$A \approx 392.02$

Therefore, Niamh has saved approximately €392 each month, rounded to the nearest euro.

We can use the formula for calculating monthly payments on a loan:

$A = P \times \frac{i(1 + i)^n}{(1 + i)^n - 1}$

Where:

• $P$ = €15,000 (loan amount)
• $i$ = 0.00866 (monthly interest rate)
• $n$ = 36 (number of payments)

Substituting these values into the formula:

$A = 15000 \times \frac{0.00866(1 + 0.00866)^{36}}{(1 + 0.00866)^{36} - 1}$

Calculating this results in:

$A \approx 487$

Thus, each of Conall's monthly payments is approximately €487.