Question

Use the compound interest formula for compounding more than once a year to determine the accumulated balance afler the stated period A $23,000 deposit at an APR of 65% with quarterly compounding for 29 years

Answer 1

To find the accumulated balance with quarterly compounding at an APR of 65% over 29 years, we plug the values into the compound interest formula: A = $23,000(1 + 0.65/4)^{4 × 29}. Compound interest significantly increases the total amount over time, especially with higher rates and longer durations.

Step-by-step explanation:

To calculate the accumulated balance after 29 years with quarterly compounding at an APR of 65%, we use the compound interest formula which accounts for the principal plus the accumulating interest. Our principal amount (P) is $23,000, the annual interest rate (r) is 65% or 0.65 in decimal form, the number of times interest is compounded per year (n) is 4 for quarterly compounding, and the time the money is invested or borrowed for (t) is 29 years. The formula we use is:

A = P(1 + r/n)nt

Let's put the values into the formula:

A = $23,000(1 + 0.65/4)4 × 29

First, we calculate 1 + r/n:

1 + 0.65/4 = 1.1625

Then, we calculate (1 + r/n)nt:

(1.1625)116

Afterward, we multiply this result by the principal $23,000 to find the accumulated balance.

Note that as the compound interest accumulates, it can make a significant difference over time, especially with such a high interest rate over a long period like 29 years.