Question - Solving Compound Interest with Quarterly Compounding
Solution:
The question refers to compound interest being calculated on a savings account. In compound interest, the interest is calculated periodically and added to the principal for the next period of interest calculation. The formula provided in the image is an expression for the total amount in the account at the end of $$ n $$ years when interest is compounded quarterly:\[ \text{Total amount} = 20,000 \left(1 + \frac{r}{1000}\right)^{4n} \]Here, $$ r $$ represents the annual interest rate (expressed as a percent) divided by the number of compounding periods in a year (which is 4 for quarterly compounding). Since the interest is compounded quarterly, the annual rate $$ r\% $$ is divided by 4 to get the rate per quarter and compounded for $$ 4n $$ times over $$ n $$ years.The question asks us to find the values of $$ r $$ and $$ n $$. However, with the given information, it is not possible to uniquely determine both variables, as we have one equation and two unknowns. Additional information, such as the final amount in the savings account or the length of the investment period, is required to solve for the individual values of $$ r $$ and $$ n $$.If further information is provided, please share it, and I can assist you in solving for the variables.
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