Lynne is 25 years old and starting an IRA (individual retirement account). She is going to invest $150 at the beginning of each month. The account is expected to earn 5.5% interest, compounded monthly. How much money, rounded to the nearest dollar, will Lynne have in her IRA if she wants to retire at age 65?
its 262,353
To calculate how much money Lynne will have in her IRA when she retires at age 65, we need to use the formula for the future value of an ordinary annuity.
The formula is: FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Payment amount per period
r = Interest rate per period
n = Total number of periods
Based on the given information:
P = $150 (the payment amount per month)
r = 5.5% annual interest rate, compounded monthly (which means the monthly interest rate is 5.5% / 12)
n = (65 years - 25 years) * 12 months per year
Now, let's plug in the values into the formula and calculate the future value:
n = (65 - 25) * 12 = 480 (months)
r = 5.5% / 12 = 0.00458 (monthly interest rate)
FV = $150 * [(1 + 0.00458)^480 - 1] / 0.00458
Calculating this value, FV ≈ $265,309.
Therefore, Lynne will have approximately $265,309 in her IRA when she retires at age 65.
To calculate the future value of Lynne's IRA, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount Lynne will have in her IRA at age 65)
P = the initial investment (the $150 that Lynne will invest at the beginning of each month)
r = the annual interest rate (5.5% or 0.055)
n = the number of times interest is compounded per year (monthly compounding, so 12)
t = the number of years of the investment (retiring at age 65, so 65 - 25 = 40 years)
Plugging in the given values into the formula:
A = 150(1 + 0.055/12)^(12*40)
Now, let's calculate this using a calculator or a spreadsheet:
A ≈ $487,677 (rounded to the nearest dollar)
Therefore, Lynne will have approximately $487,677 in her IRA if she wants to retire at age 65.
40 years *12 = 480 months = n
.055/12 = .0045833333 interest rate per month = r
N = 150 per month in
amount of sinking fund
S = N [(1 + r)^n -1] /r
S = 150 [ (1.0045833333^480 -1 ) ] / 0.0045833333
= 150 [ 7.979765 ] /0.0045833333
= 150 ( 1741.04)
= 261,156