Final answer:
To find out how much Bryn will owe after 14 years on a loan of £800 with a compound interest rate of 28% per year, we apply the compound interest formula and calculate that she will owe approximately £11,408.
Step-by-step explanation:
The question is asking to determine the amount of money Bryn will owe after 14 years if she takes out a loan of £800 with a compound interest rate of 28% per year.
To calculate the future value of the loan, we use the compound interest formula, which is:
FV = PV (1 + r)^n
Where:
FV is the future value of the loan,
PV is the present value or initial amount of the loan (£800),
r is the annual interest rate (28%, or 0.28),
n is the number of years the interest is compounded (14).
Plugging in the numbers:
FV = £800 * (1 + 0.28)^14
Calculating that we get:
FV = £800 * (1.28)^14
FV = £800 * 14.26 (rounded to two decimals)
FV = £11,408
Therefore, after 14 years, Bryn will owe approximately £11,408.