QuestionJuly 21, 2025

1. An amount 5000 earns interest at 3% per year. (a) What will this amount have grown to after ten years? (b) How long does it take for the 5000 to double?

1. An amount 5000 earns interest at 3% per year. (a) What will this amount have grown to after ten years? (b) How long does it take for the 5000 to double?
1. An amount 5000 earns interest at 3% per year. (a) What will this amount have grown to after ten years? (b) How long does it take for the 5000 to double?

Solution
3.2(253 votes)

Answer

(a) \ 6715.47 ### (b) Approximately 23.45 years Explanation 1. Calculate future value after ten years Use the formula for compound interest: A = P(1 + r)^t, where P = 5000, r = 0.03, and t = 10. Calculate A. 2. Solve for time to double the amount Set A = 2P in the compound interest formula: 2P = P(1 + r)^t. Simplify to 2 = (1 + r)^t. Solve for t using logarithms: t = \frac{\log(2)}{\log(1 + r)}.

Explanation

1. Calculate future value after ten years<br /> Use the formula for compound interest: $A = P(1 + r)^t$, where $P = 5000$, $r = 0.03$, and $t = 10$. Calculate $A$.<br /><br />2. Solve for time to double the amount<br /> Set $A = 2P$ in the compound interest formula: $2P = P(1 + r)^t$. Simplify to $2 = (1 + r)^t$. Solve for $t$ using logarithms: $t = \frac{\log(2)}{\log(1 + r)}$.
Click to rate:

Similar Questions