Question

Carlos deposited $25,000 into a fund at the beginning of every quarter for 12 years. She then stopped making deposits into the fund and allowed the investment to grow for 6 more years. The fund was growing at 5.02% compounded monthly.

a. What was the accumulated value of the fund at the end of year 12 ?

Answer 1

The accumulated value of the fund at the end of year 12 is approximately $58,798.88.

Step-by-step explanation:

To calculate the accumulated value of the fund at the end of year 12, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the accumulated value
• P is the principal (initial deposit)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, Carlos deposited $25,000 at the beginning of every quarter for 12 years, so the total number of times interest is compounded per year (n) is 4. The annual interest rate (r) is 5.02% or 0.0502. The number of years (t) is 12.

Plugging in these values:

A = $25,000(1 + 0.0502/4)^(4*12)

Simplifying the equation:

A = $25,000(1.01255)^(48)

Calculating:

A ≈ $58,798.88

Therefore, the accumulated value of the fund at the end of year 12 is approximately $58,798.88.