Question

(a) Patty Stacey deposits $2200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 6%, compounded annually. (Round your answer to the nearest cent.) (b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $2200 deposits at the end of each of the next 15 years. If the interest rate is 6%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)

Answer 1

a)

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This situation can considered as an annuity for first years
and then accumulating the amount using compound interest

Contribution 2200
Interest Rate 6%
Value of IRA after first 5 years
Annuity Formula is,
A = P*[(1+i)^n - 1]/ i
A is Amount
P is Annual
Contribution
i is interest rate
n is number of years

or, A=2200 *[1.06^5-1]/0.06
= 12401.60

Next the amount was accumulated for 25 years Value after 25 years can be calculated as

Amount Principal* (1+ i)^n
n here is 25 years, rest all remain same and Principal is value of IRA account at the end of 5 years
which is $12401.60

Value of IRA after 30 years 12401.60 * 1.06^25 = 53226.08 dollers

b)

In the husband's case, all data are same expect the timelines
He starts investing 10 years later.
he invests for 15 years and accumulates for next 5 years

Value of IRA after 25 years, that is 10 years plus 15 years
of investment 2200*[ 1.06^15-1] /0.06 =51207.13

Value of IRA after 30 years = 51207.13 * 1.06^5 = $ 68256.70