Question

It is more realistic to invest each month for retirement at age 67 if you are now 25. Assume you can find an investment that will pay 3% annually and you want to accumulate $1,000,000. How much would you need to invest each month?

Answer 1

So monthly you need to deposit $992.11

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So in this question we already know the FV of annuity which is 1000000, rate of interest is 3% per annum or (3/12 = 0.25% per month), time will be (12* 42 = 504 months), we need to find the annuity amount.

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

Let's put the values in the formula,

1000000 = x[(1 + 0.0025)^504 - 1]/ 0.0025

1000000 = x[(1.0025 )^504 - 1]/ 0.0025

1000000 = x (3.51988254124206) - 1/ 0.0025

1000000 = x (2.51988254124206)/ 0.0025

1000000 = x * 1007.95301649682

X = 1000000 / 1007.95301649682

X = 992.11

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Hope that helps.

Feel free to comment if you need further assistance J