use the present value formula to determine the amount to be invested now, or the present value needed.\nthe…

use the present value formula to determine the amount to be invested now, or the present value needed.\nthe desired accumulated amount is $70,000 after 13 years invested in an account with 2.9% interest compounded monthly.\n\nthe amount to be invested now, or the present value needed, is $□.\n(round to the nearest cent as needed.)

use the present value formula to determine the amount to be invested now, or the present value needed.\nthe desired accumulated amount is $70,000 after 13 years invested in an account with 2.9% interest compounded monthly.\n\nthe amount to be invested now, or the present value needed, is $□.\n(round to the nearest cent as needed.)

Answer

Answer:

$$49,153.33$

Explanation:

Step1: Define given values

$A = 70000$, $r = 0.029$, $n = 12$, $t = 13$

Step2: Recall present value formula

$$P = A\left(1+\frac{r}{n}\right)^{-nt}$$

Step3: Calculate the rate per period

$\frac{r}{n} = \frac{0.029}{12} \approx 0.0024167$

Step4: Calculate total compounding periods

$nt = 12 \times 13 = 156$

Step5: Compute the growth factor

$\left(1+0.0024167\right)^{-156} \approx 0.70219$

Step6: Find present value

$P = 70000 \times 0.70219 \approx 49153.33$