Question

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You just found out that your retirement fund is losing money at an annual rate of 6.3% compounded quarterly. Currently, you have $56,700 in the account.

a. Write an equation to show how much money will be in the account for any number of years.

b. How much will the account be worth after 14 years? Show or explain how you know.

Answer 1

• The equation for the value of the account for any number of years would be:

A = P * (1 - r)^(t/n)

Where:

A = the final value of the account

P = the initial value of the account ($56,700)

r = the annual interest rate (6.3%)

t = the number of years

n = the number of compounding periods per year (4)

So, the equation would be:

A = 56,700 * (1 - 0.063)^(t/4)

• To find out how much the account will be worth after 14 years, we can plug in 14 for t in the equation above:

A = 56,700 * (1 - 0.063)^(14/4)

A = $24,988.18

So, the account will be worth $24,988.18 after 14 years, if the rate of loss stays 6.3% compounded quarterly.