Compound Interest Calculation Result
The question in the image asks to calculate the amount of money that Adam will have in the bank account after 24 years with an initial deposit of £3,660 and an annual compound interest rate of 3.25%.
To solve this, we use the formula for compound interest, which is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
\( A \) = the amount of money accumulated after n years, including interest.
\( P \) = the principal amount (the initial amount of money).
\( r \) = the annual interest rate (decimal).
\( n \) = the number of times that interest is compounded per year.
\( t \) = the time the money is invested for, in years.
In this case:
\( P = £3,660 \)
\( r = 3.25\% = 0.0325 \) (in decimal form)
\( n = 1 \) (interest is compounded once per year)
\( t = 24 \) years
Substituting these values into the formula gives us:
\( A = £3,660 \left(1 + \frac{0.0325}{1}\right)^{1 \times 24} \)
\( A = £3,660 \left(1 + 0.0325\right)^{24} \)
\( A = £3,660 \times 1.0325^{24} \)
Now we need to calculate \( 1.0325^{24} \) and multiply it by £3,660 to find the final amount.
\( 1.0325^{24} \approx 2.0398873 \) (rounded to 7 decimal places for precision)
Now, we will multiply this by the principal amount:
\( A \approx £3,660 \times 2.0398873 \)
\( A \approx £7,465.97 \) (rounded to two decimal places)
After 24 years, Adam will have approximately £7,465.97 in the account.
