Question - Compound Interest Calculation Result
Solution:
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)$$ t = 24 $$ yearsSubstituting 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.
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