Question
Future value (with changing years). Dixie Bank offers a certificate of deposit with an option to select
your own investment period. Jonathan has
for his CD investment. If the bank is offering a
interest rate, compounded annually, how much will the CD be worth at maturity if Jonathan picks a
a. three-year investment period?
b. five-year investment period?
c. ten-year investment period?
d. twenty-year investment period?
your own investment period. Jonathan has
interest rate, compounded annually, how much will the CD be worth at maturity if Jonathan picks a
a. three-year investment period?
b. five-year investment period?
c. ten-year investment period?
d. twenty-year investment period?
Ask by Carroll Gardner. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The future values of the CD for different investment periods are:
a. Three years: $8,682.19
b. Five years: $9,572.11
c. Ten years: $12,216.71
d. Twenty years: $19,899.73
a. Three years: $8,682.19
b. Five years: $9,572.11
c. Ten years: $12,216.71
d. Twenty years: $19,899.73
Solution
To calculate the future value of the certificate of deposit (CD) with a changing investment period, we can use the formula for compound interest:
where:
-
is the future value of the investment -
is the present value of the investment (initial amount) -
is the annual interest rate -
is the number of years the money is invested
Given:
- Initial amount (present value) = $7,500
- Annual interest rate = 5% = 0.05
- We need to calculate the future value for different investment periods:
a. Three-year investment period
b. Five-year investment period
c. Ten-year investment period
d. Twenty-year investment period
Let’s calculate the future value for each investment period:
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Add the numbers:
- step2: Convert the expressions:
- step3: Evaluate the power:
- step4: Multiply:
a. For a three-year investment period, the future value of the CD will be $8682.1875.
Now, let’s calculate the future value for the remaining investment periods:
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Add the numbers:
- step2: Convert the expressions:
- step3: Simplify:
- step4: Rewrite the expression:
- step5: Reduce the numbers:
- step6: Rewrite the expression:
- step7: Rewrite the expression:
- step8: Rewrite the expression:
- step9: Reduce the numbers:
- step10: Multiply:
b. For a five-year investment period, the future value of the CD will be $9572.11171875.
Now, let’s calculate the future value for the remaining investment periods:
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Add the numbers:
- step2: Convert the expressions:
- step3: Simplify:
- step4: Rewrite the expression:
- step5: Reduce the numbers:
- step6: Rewrite the expression:
- step7: Rewrite the expression:
- step8: Rewrite the expression:
- step9: Reduce the numbers:
- step10: Multiply the fractions:
c. For a ten-year investment period, the future value of the CD will be approximately $12216.709701.
Now, let’s calculate the future value for the remaining investment period:
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Add the numbers:
- step2: Convert the expressions:
- step3: Simplify:
- step4: Rewrite the expression:
- step5: Reduce the numbers:
- step6: Rewrite the expression:
- step7: Rewrite the expression:
- step8: Rewrite the expression:
- step9: Reduce the numbers:
- step10: Multiply the fractions:
d. For a twenty-year investment period, the future value of the CD will be approximately $19899.732789.
Therefore, the future values of the CD for different investment periods are:
a. Three-year investment period: $8682.1875
b. Five-year investment period: $9572.11171875
c. Ten-year investment period: $12216.709701
d. Twenty-year investment period: $19899.732789
a. Three-year investment period: $8682.1875
b. Five-year investment period: $9572.11171875
c. Ten-year investment period: $12216.709701
d. Twenty-year investment period: $19899.732789
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Extra Insights
To calculate the future value of Jonathan’s certificate of deposit (CD) for different investment periods, we can use the formula for compound interest:
Where:
-
= Future Value -
= Principal Amount (initial investment, ) -
= Annual interest rate (5%, or 0.05) -
= Number of years
Let’s calculate:
a. For the three-year investment period:
b. For the five-year investment period:
c. For the ten-year investment period:
d. For the twenty-year investment period:
In summary:
- After 3 years: approximately
- After 5 years: approximately
- After 10 years: approximately
- After 20 years: approximately