Marcus receives an inheritance of ​$5000. He decides to invest this money in a 18​-year certificate of deposit​ (CD) that pays 5.0​% interest compounded monthly. How much money will Marcus receive when he redeems the CD at the end of the 18 ​years?



Answer :

Answer:

o determine how much money Marcus will receive at the end of 18 years from his $5000 investment in a certificate of deposit (CD) that pays 5.0% interest compounded monthly, we can use the formula for compound interest:

=

(

1

+

)

A=P(1+

n

r

)

nt

where:

A is the amount of money accumulated after

t years, including interest.

P is the principal amount (the initial sum of money).

r is the annual interest rate (decimal).

n is the number of times the interest is compounded per year.

t is the time the money is invested for in years.

Given:

=

5000

P=5000 (the initial investment)

=

0.05

r=0.05 (5.0% annual interest rate)

=

12

n=12 (interest is compounded monthly)

=

18

t=18 (the investment duration in years)

Plugging in the values:

=

5000

(

1

+

0.05

12

)

12

×

18

A=5000(1+

12

0.05

)

12×18

First, we calculate the monthly interest rate:

0.05

12

=

0.0041667

12

0.05

=0.0041667

Next, we calculate the exponent

12

×

18

12×18:

12

×

18

=

216

12×18=216

Now, we substitute these values back into the formula:

=

5000

(

1

+

0.0041667

)

216

A=5000(1+0.0041667)

216

=

5000

(

1.0041667

)

216

A=5000(1.0041667)

216

Using a calculator to evaluate the expression:

(

1.0041667

)

216

2.432364

(1.0041667)

216

≈2.432364

Finally, we multiply this result by the principal:

=

5000

×

2.432364

12161.82

A=5000×2.432364≈12161.82

Therefore, Marcus will receive approximately $12,161.82 when he redeems the CD at the end of the 18 years.

Step-by-step explanation: