How much do you need to invest annually, at 5.2%, to reach retirement savings of $130,988.87 in 11 years?

To determine how much you need to invest annually to reach a specific retirement savings goal, you can use the future value of an annuity formula, which is commonly applied in finance. The formula is:

[

FV = P \frac{(1 + r)^n - 1}{r}

]

where:

• (FV) is the future value of the annuity (in this case, $130,988.87),

• (P) is the annual payment (the amount you are trying to find),

• (r) is the annual interest rate (5.2%, or 0.052 when expressed as a decimal),

• (n) is the number of years (11 years in this case).

Rearranging the formula to solve for (P), we have:

[

P = \frac{FV \cdot r}{(1 + r)^n - 1}

]

Plugging in the values:

• (FV = 130,988.87)

• (r = 0.052)

• (n = 11)

Calculating:

1. Calculate ((1 + r)^n):

[

(1 + 0