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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: