425,578 views
30 votes
30 votes
You want to have $150,000 in your retirement account when you retire in 30 years. Your retirement account earns 7%

interest. How much do you need to deposit each month to meet your retirement goal?
Round your answer to the nearest cent.
Do NOT include the dollar sign.

User Tom Squires
by
2.6k points

2 Answers

26 votes
26 votes

Answer:

Explanation:

Since we're talking about making a deposit of a certain amount every month rather than just one big deposit, we are talking about an annuity. The formula for the value of an annuity is A(t)=d[(1+rn)nt−1](rn) where A(t) is the value of the annuity, d is the amount of each deposit, n is the number of deposits per year, t is the number of years, and r is the rate of interest. In this case we know we want the value of the annuity to be A(t)=$150,000, we want to make deposits every month, or 12 times a year, so n=12, we want to reach our desired value in 30 years, so t=30, and our account earns 7% interest, so r=0.07. We can plug in all of these values and solve for d to find the amount we need to deposit each month:

A(t)150,000150,000150,000d=d[(1+rn)nt−1](rn)=d[(1+0.0712)12⋅30−1]0.0712≈d[(1.00583)360−1]0.00583≈1,219.97d≈122.95

The amount you need to deposit each month is approximately $122.95.

User GerardBeckerleg
by
2.8k points
24 votes
24 votes

Answer: 123.05

Use annuity formula

User Oldbeamer
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2.8k points