Question

Me Unuwing table shows the average returns for some of the largest mutual funds commonly found in retirement plans. (Assume end-of-month deposits and withdrawals and monthly compounding, and assume that the quoted rate of return continues indefinitely.) Mutual Fund Fidelity Growth Company Vanguard 500 Index PIMCO Total Return Vanguard Total Bond Market Index Rate of Return 14.83% 13.25% 2.77% 2.67% Type Stock fund Stock fund Bond fund Bond fund For the past 15 years you have been depositing $400 per month in the Vanguard bond fund, and you have now transferred your current balance to the PIMCO bond fund, where you plan to continue depositing $400 per month until you retire in 20 years. How much can you anticipate having in the investment when you retire? HINT (See Example 1.) (Round your answer to the nearest cent.)

Answer 1

For past 15 years,

Deposit of $400 at the end of every month in Vanguard 500 index for 15 years. So it is an ordinary annuity with

PMT = 400

n = 12 period in a year

t = 15 years

r = 2.67% p.a. compounded monthly

Value of all the deposits today can be calculated using formula FV = PMT*((1+r/n)^(n*t) - 1)/(r/n)

So, value today = 400*((1+0.0267/12)^(12*15) - 1)/(0.0267/12) = $88432.70

So current balance = $88432.70

now this balance is transferred to PIMCO bond fund. Also, monthly deposit of $400 is now made in this fund for next 20 years.

Value of fund at retirement = FV of current balance + FV of annuity deposits

FV of current balance = PV*(1+r/n)^(n*t)

here, r = 2.77% p.a. compounded monthly

t = 20 years

So, FV of current balance = 88432.70*(1+0.0277/12)^(20*12) = $153792.36

FV of annuity deposits = PMT*((1+r/n)^(n*t) - 1)/(r/n)

So, FV of annuity deposits = 400*((1+0.0277/12)^(12*20) - 1)/(0.0277/12) = $128073.23

Value of fund at retirement = 153792.36 + 128073.23 = $281865.60