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Question 10
1 pts
Lois Smith wants to retire in California when she is 70
years of age. Lois, who is now 50, believes she will need
$400,000 to retire comfortably. To date, she has set
aside no retirement money. If she get an interest rate of
8% compounded semiannually, she will have to invest
(blank) today.
$38,000
• $83,320
$38,320
O none of the above​

Respuesta :

lucic

Answer:

$83,320

Step-by-step explanation:

The formula to apply here is;

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

where;

A=Amount at the end

P=the amount to invest/principal

r=rate of interest as a decimal

n=number of compoundings in a year

t=time in years

Given that;

A=$400,000

P=?

r=8%=0.08

n=2

t=20

Substitute values in equation

[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\400,000=P(1+\frac{0.08}{2} )^{2*20} \\\\\\400,000=P(1+0.04)^{40} \\\\\\\\400,000=P(1.04)^{40} \\\\\\400,000=P(4.80102062794)\\\\\\\\\frac{400,000}{4.80102062794} =\frac{4.80102062794P}{4.80102062794} \\\\\\83315.617=P\\\\[/tex]

P=$83,320 (to the nearest dollar)

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