Question

In: Finance

2. On your birthday, when you turned 22, $23700 was deposited in an account which earns...

2. On your birthday, when you turned 22, $23700 was deposited in an account which earns 7.25% compounded annually.

a. How much can you withdraw annually for 18 years if the first withdrawal is made on the day you become 47?

b. State the total amount of interest earned on this account.

Expert Solution

First, let us find the amount accumulated in the account when you turned 47.

We can use the future value formula:

Where,
FV= Future value
PV =Present value
i = rate of interest in decimal form (i.e 7.25% = 0.0725)
n = number of years (47 - 22 =25)

Therefore,

a) Now we can use the present value of the annuity due formula to find the annual withdrawal.

Where,
PVA = Present value of the annuity
A = Annual withdrawal
i = Interest rate in decimal form
n = Number of years (18)

Therefore,

Therefore, annual withdrawal is $12,868.34.

b) Total amount withdrawn = 12,868.34 * 18 = $231,630.03

Amount invested = $23,700

Total amount of interest earned = Total amount withdrawn - Amount invested

= $231,630.03 - $23,700

= $207,930.03

jeff jeffy answered 2 years ago

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