Mathematics: Question 101 ptslois smith wants to retire in california when she is 70years of age. lois, who is now 50, believes she will need$400,000 to retire comfortably. to date, she has setaside no retirement money. if she get an interest rate of8% compounded semiannually, she will have to invest(blank) today.$38,000• $83,320$38,320o none of the above

Question 101 ptslois smith wants to retire in california

Ответ:

Lacey9319

16.03.2022

Mathematics

$83,320

Step-by-step explanation:

The formula to apply here is;

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

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

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

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

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