Question

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​

Answer 1

$83,320

Explanation:

The formula to apply here is;

`A=P(1+(r)/(n) )^(nt)`

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

`A=P(1+(r)/(n) )^(nt) \\\\\\400,000=P(1+(0.08)/(2) )^(2*20) \\\\\\400,000=P(1+0.04)^(40) \\\\\\\\400,000=P(1.04)^(40) \\\\\\400,000=P(4.80102062794)\\\\\\\\(400,000)/(4.80102062794) =(4.80102062794P)/(4.80102062794) \\\\\\83315.617=P\\\\`

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