Question

An employee wants to invest $60,000 in a pension plan. One investment offers 4% compounded quarterly. Another offers 3.25% compounded continuously.

(a) Which investment will earn more interest in 4ут? (b) How much more will the better plan earn?

Answer 1

a) The second investment offering 3.25% compounded continuously will earn more interest.

b) The better plan will earn an additional amount of $141.85.

Step-by-step explanation:

To determine which investment will earn more interest in 4 years, we need to calculate the future value of each investment.

For the first investment offering 4% compounded quarterly:

1. Calculate the interest rate per quarter: 4% divided by 4 = 1%.
2. Convert the number of quarters to years: 4 years multiplied by 4 = 16 quarters.
3. Calculate the future value using the compound interest formula: $60,000 multiplied by (1 + 0.01)^16 = $71,631.52.

For the second investment offering 3.25% compounded continuously:

1. Calculate the continuous interest rate using the formula: e^(0.0325) - 1 = 0.033.
2. Calculate the future value using the continuous compound interest formula: $60,000 multiplied by e^(0.033 * 4) = $71,773.37.

(a) Comparing the two investments:

The second investment offering 3.25% compounded continuously will earn more interest in 4 years.

(b) Calculation of the extra earnings:

The better plan will earn an additional amount of $71,773.37 - $71,631.52

= $141.85.