Question

You are planning to invest $ 5,000 in an account earning 9​% per year for retirement. (a) If you put the $ 5,000 in an account at age​ 23, and withdraw it 42 years​ later, how much will you​ have? (b) If you wait 10 years before making the​ deposit, so that it stays in the account for only 32 ​years, how much will you have at the​ end?

Answer 1

a). You will have a total of $186,587.66 at the end of 42 years

b). You will have total of $78,816.64 at the end of 32 years

Step-by-step explanation:

a). How much you will earn after 42 years

Step 1: Determine amount earned in 42 years

The total amount earned can be expressed as;

A=P(1+r)^n

where;

A=total amount earned

P=Initial investment amount

r=Annual interest rate

n=number of years of investment

In our case;

P=$5,000

r=9%=9/100=0.09

n=42 years

replacing;

A=5,000(1+0.09)^42

A=5,000(1.09)^42

A=186,587.66

You will have a total of $186,587.66 at the end of 42 years

b). Amount after 32 years

where;

P=5,000

r=9%=9/100=0.09

n=32 years

replacing;

A=5,000(1+0.09)^32

A=5,000(1.09)^32

A=78,816.64

You will have total of $78,816.64 at the end of 32 years