Meagan invests $1,200 each year in an IRA for 12 years in an account that earned
ID: 2761557 • Letter: M
Question
Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5% compounded annually.
At the end of 12 years, she stopped making payments to the account, but continued to invest her accumulated amount at 5% compounded annually for the next 11 years.
a. What was the value of the Ira at the end of 12 years?
b. What was the value of the investment at the end of the next 11 years?
c. How much interest did she earn?
Please Show your work AND explain your reasoning using complete English sentences
I-Prt NE A P(1+rt) 1-1 ntExplanation / Answer
Solution:
a.
Since the invested amount is same for 12 years. It is a ordinary annuity series. The future value annuity factor is calculated by the following formula:
Here, R is Rate of Interest and n = no. of payments
FVIFA (R%, n) = [(1+R)n – 1] / R
The Value of the Ira at the end of 12 years = Annual Investment Amount x [(1 + 0.05)12 – 1]/0.05
= $1,200 x [(1.79585 – 1)/0.05]
= $1,200 x 15.917
= $19,100.55
b.
The value of investment at the end of the next 11 years (i.e. at the end of 23 years) = Value of Ira at the end of 12th year as calculated above + $19,100.55 x (1 + 0.05)23-12
= $19,100.55 + $19,100.55 x (3.07152 - 1.795856)
= $19,100.55 + $24,365.95
= $43,466.50
c.
Interest she earns = Total Investment value at the end of 23rd year – Amount invested in 12 years
= $43,466.50 – ($1,200 x 12)
= $43,466.50 - $14,400
= $29,066.50