Solve the problem. Round to the nearest cent.
Joan wants to have $250,000 when she retires in 27 years. How much should she invest annually in her annuity to do this if the interest is 7% compounded annually?
A) $1861.10
B) $3356.43
C) $2672.15
D) $937.86
x( 1.07^27 - 1)/.07 =25000
x(74.483823..) = 250000
x = $ 3356.43
To solve this problem, we can use the formula for the future value of an annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the annual investment amount
r is the interest rate per period
n is the number of periods
In this case, the future value (FV) is $250,000, the interest rate (r) is 7% compounded annually (0.07), and the number of periods (n) is 27.
Let's calculate the annual investment amount (P) by rearranging the formula:
P = FV * (r / [(1 + r)^n - 1])
Substituting the given values:
P = $250,000 * (0.07 / [(1 + 0.07)^27 - 1])
Now, let's solve this equation to find the annual investment amount.
P = $250,000 * (0.07 / [1.07^27 - 1])
P = $250,000 * (0.07 / [3.864905132 - 1])
P = $250,000 * (0.07 / 2.864905132)
P ≈ $1861.10
Rounding to the nearest cent, the answer is option A) $1861.10.