Question

Diane invests some money into an investment account that pays 3.4% annual interest compounded quarterly. After 20 years. The investment account increased to 7.872,86. What was Diane’s initial investment?

Answer 1

To find Diane's initial investment, we need to use the formula for compound interest:

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

where:

A = 7,872.86 (final amount)

P = initial investment

r = 3.4% (annual interest rate)

n = 4 (number of times interest is compounded per year)

t = 20 (number of years)

We can now rearrange the formula to solve for P:

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

Plugging in the values, we get:

P = 7,872.86 / (1 + 3.4% / 4)^(4 * 20)

P = 7,872.86 / 1.008622^80

P = 7,872.86 / 1.854148

P = 4,228.44

So Diane's initial investment was $4,228.44.

Explanation: