Question

You currently have $80,000 in your retirement account. Twenty-five years from now, you hope to bring up the value of your retirement account to $1.1 million. In order to make this happen, you want to make regular deposits in equal amounts each month (that is, you will make 300 equally-sized deposits, with one each month, for the next 25 years). If interest rates are .5% per month, how much will you have to deposit each month in order to hit your retirement goal in 25 years?

A. $1,071.87
B. $1,587.32
C. $4,785.89
D. $17,371.51
E. $38,004.89

Answer 1

To reach the retirement goal of $1.1 million in 25 years with a monthly interest rate of 0.5%, the student must make a monthly deposit of approximately $1,071.87, which adjusts the future value needed after accounting for the growth of the existing $80,000.

Step-by-step explanation:

The student's question involves finding out how much to deposit each month in a retirement account to reach $1.1 million in 25 years at an interest rate of 0.5% per month. This is a problem of future value of an annuity, which can be solved using the future value annuity formula:

FV = P * [((1 + r)^n - 1) / r]

Where:

• FV is the future value of the account.
• P is the monthly payment.
• r is the monthly interest rate.
• n is the total number of payments.

Given that:

• FV = $1,100,000
• r = 0.5% or 0.005 when expressed as a decimal
• n = 25 years * 12 months/year = 300

The existing balance in the account is $80,000, which also grows at the same rate of interest, separate from the deposits. To find P, we use the future value of an annuity formula, adjusting FV for the growth of the initial $80,000:

New FV = $1,100,000 - $80,000 * (1 + 0.005)^300

After calculating the new FV, we can solve for P:

P = New FV / [((1 + 0.005)^300 - 1) / 0.005]

Through calculation, we find that the required monthly deposit to achieve the retirement goal in 25 years is approximately $1,071.87, which corresponds to option A.