Question

You have just deposited $35,000 into a retirement account. You expect to make monthly deposits of $350 into this account over the next 40 years. For the first 25 year, you plan to pursue an aggressive investment approach, with an average annual rate of return of 12%. After that, you plan to become more conservative, and earn an annual rate of return of 6% for the remaining 15 years. How much money will you have in your account when you retire 40 years from now?

Answer 1

Initial deposit = 35,000

Rate₁ for 25 years = 12% | Rate₂ for remaining 15 years = 6%

Future Value of Deposit at 25 years = Deposit * (1+R₁)²⁵ = 35000 * (1+12%)²⁵ = 595,002.25

Future Value of Deposit at 40 years = FV of deposit at 25 years * (1 + R₂)¹⁵ = 595,002.25 * (1+6%)¹⁵ = 1,425,957.53

Monthly payment = 350

Rate₁ for 25 years = 12% | Rate₂ for remaining 15 years = 6%

Using Future Value of Annuity formula: FV = (PMT / r) * [(1+r)ⁿ - 1]

Since it is monthly payment, R will become R/12 and Time will become T*12

For example, R for 25 years becomes 12% / 12 = 1% and Time = 25*12 = 300

FV of Monthly payment at 25 years = (350 / 1%) * [(1+1%)³⁰⁰ - 1] = 657,596.32

Since 657,596.32 is at 25 years, hence, we will compound it with 6% rate to its Future Value at 40 years

FV at 40 of 657,596.32 = 657,596.32*(1+6%)¹⁵ = 1,575,967.85

Now for remaining 15 years R will become 6% / 12 = 0.5% and Time will become 15*12 = 180

FV of Monthly Payment for next 15 years (at 40 years) = (350 / 0.5%) * [(1+0.5%)¹⁸⁰ - 1] = 101,786.55

Using all the values made bold above will be added to find the total money in account at the time of retirement

Total money at retirement = FV of Initial deposit at 40 + FV of Initial 25 yrs Annuity at 40 + FV of remaining 15 yrs annuity at 40 = 1,425,957.53 + 1,575,967.85 + 101,786.55 = $ 3,103,711.93

answered by: anonymous