Question

Determine the amount of money that must be invested now​ (time 0) at 10​% nominal​ interest, compounded​ monthly, to provide an annuity of ​$7 comma 000 per year for 12 ​years, starting eight years from now. The interest rate remains constant over this entire period of time.

Answer 1

Answer:

the amount of money that must be invested now is $21068.87

Explanation:

Given that:

Nominal interest = 10%

Annuity = 7000

n = 8 years

The Effective interest rate is calculated by using the formula:

Effective interest rate = $( 1 + \dfrac{r}{100 \times n})^n-1$

Effective interest rate = $( 1 + \dfrac{10}{100 \times 8})^8-1$

Effective interest rate = 0.1045

Effective interest rate = 10.45 %

Thus ; the the amount of money that must be invested now​  is the present value with the annuity of ​$7, 000 per year for 12 ​years, starting eight years from now.

$PV = 7000(\dfrac{(1+ 0.1045)^{12}-1}{0.1045(1 + 0.1045)^{12}})( \dfrac{1}{(1+ 0.1045)^8})$

PV = 7000 × 6.666056912 × 0.4515171371

PV = $21068.87

Thus; the amount of money that must be invested now is $21068.87