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?

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

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

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