Answer :
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 = [tex]( 1 + \dfrac{r}{100 \times n})^n-1[/tex]
Effective interest rate = [tex]( 1 + \dfrac{10}{100 \times 8})^8-1[/tex]
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.
[tex]PV = 7000(\dfrac{(1+ 0.1045)^{12}-1}{0.1045(1 + 0.1045)^{12}})( \dfrac{1}{(1+ 0.1045)^8})[/tex]
PV = 7000 × 6.666056912 × 0.4515171371
PV = $21068.87
Thus; the amount of money that must be invested now is $21068.87