Question

Calculate the amount of interest earned in 8 years on $16,000 deposited in the account paying 10% Annual interest compounded quarterly. Round to the nearest cent

Answer 1

To calculate the amount of interest earned in 8 years on a $16,000 deposit at 10% annual interest compounded quarterly, use the formula for compound interest.

Step-by-step explanation:

To calculate the amount of interest earned in 8 years on a $16,000 deposit at 10% annual interest compounded quarterly, we can use the formula for compound interest:

Compound Interest = Principal Amount × (1 + (Annual Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods × Number of Years)

In this case, the principal amount is $16,000, the annual interest rate is 10%, the number of compounding periods per year is 4 (quarterly compounding), and the number of years is 8:

Compound Interest = $16,000 × (1 + (0.10 / 4))^(4 × 8)

Using this formula and rounding to the nearest cent, the amount of interest earned would be $12,425.76

Answer 2

Compound Interest

The final value of an investment P deposited at an interest rate r for t years is:

`FV=P\cdot(1+(r)/(m))^(t\cdot m)`

Where m is the number of times the investment earns interest in a year (compounding times per year).

In the problem, P = $16,000, r = 10% = 0.1, t = 8, and m = 4 (there are 4 quarters in a year).

Applying the formula:

`\begin{gathered} FV=\$16,000\cdot(1+(0.1)/(4))^(4\cdot8) \\ \text{Operating:} \\ FV=\$16,000\cdot(1.025)^(32) \\ FV=\$16,000\cdot2.20376 \\ FV=\$35,260.11 \end{gathered}`

Now we can calculate the amount of interest earned by subtracting:

I = FV - P

I = $35,260.11 - $16,000

I = $19,260.11