Question

QUESTION 34 Linda wants to retire in 27 years with $2,000,000 in her IRA. She plans to invest $20,000 a year into the account until she retires. About what rate of interest must Linda earn on the IRA to meet her goal? 8.84% 9.21% 10.11% 10.58%

Answer 1

Given: n=27years, P(annual payments)=20000, FV of annuity =2000000

FVAF=p[(1+r)^n-1/r]

since rate of interest is given , try all interest rates into the above formula to get the answer closest to 2000000.

1)8.84%

=20000[(1+0.0884)^27-1/(0.0884)]

=2001514.234

2)9.21%

=20000[(1+0.0921)^27-1/(0.0921)]

2126293.

3)10.11%

=20000[(1+0.1011)^27-1/(0.1011)]

=2466588.

4)10.58%

=20000[(1+0.1058)^27-1/(0.1058)]

=2667319.

Hence closest is 8.84%,

you can also try in excel , function to be used is Rate(27,-20000,0,(2000000))

you get 9% closest to 8.84%