Question

You have two different savings accounts. For Account A, the interest earned after 18 months is $12.00. For Account B, the interest earned after 27 months is $27.00. a. If the interest rate is 3.2% for Account A, how much is the principal? b. If the interest rate is 2.4% for Account B, how much is the principal? c. Which account earned you the most interest in the first year? Explain.

Answer 1

For this question we need to use the formula for compound interest:

$P=P_0(1+\frac{i}{n})^{nt}$

Where P is the final value, P0 is the initial value, i is the interest rate, t is the time in years and n is a value that depends on the compound rate (let's assume that is monthly, so we have n = 12)

Calculating the principal (P0) for account A, using the interest (P - P0) equal 27, we have:

$\begin{gathered} P-P_0=P_0(1+\frac{0.032}{12})^{18}-P_0 \\ 12=P_0(1.00266667)^{18}-P_0 \\ 12=P_0(1.049-1) \\ P_0=244.90 \end{gathered}$

So the principal for account A is $244.90.

For account B, we have:

$\begin{gathered} 27=P_0(1+\frac{0.024}{12})^{27}-P_0_{} \\ 27=P_0(1.055-1) \\ P_0=490.91 \end{gathered}$

The principal for account B is $490.91.