Question

Suppose 10 year ago your mother deposited $3400 in an investment account earning 5% a year. After 3 years she withdrew $1,122. There were no additional deposits or withdrawals. Obtain today's value of the investment account?

A. $4,239.39

B. $3,959.48

C. $,416.24

D. $3,710.62

Answer 1

Option (B) is correct

First we will calculate the value after 3 years of invetsment.. We will use the following future value formula:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $3400, r = rate of interest = 5%, n= time period = 3

now, putting theses values in the above equation, we get,

FV = $3400 * (1 + 5%)3

FV = $3400 * (1 + 0.05)3

FV = $3400 * (1.05)3

FV = $3400 * 1.157625

FV = $3935.925

So, value after 3 years was $3935.925.

Now, $1122 is withdrawan from the account. So, the balance in the account is:

Balance = $3935.925 - $1122 = $2813.925

Now, we will calculate the value of investment today in the same manner as above:

FV = PV * (1 + r%)n

where, FV = Future value, PV = Present value = $2813.925, r = rate of interest = 5%, n= time period = 10 - 3 = 7

now, putting theses values in the above equation, we get,

FV = $2813.925 * (1 + 5%)7

FV = $2813.925 * (1 + 0.05)7

FV = $2813.925 * (1.05)7

FV = $2813.925 * 1.40710042266

FV = $3959.476

So, value of investment now is $3959.48