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Interest Greg Tobin wishes to invest a $5000 bonus check
Chapter 2, Problem 22A(choose chapter or problem)
Problem 22A
Interest Greg Tobin wishes to invest a $5000 bonus check into a savings account that pays 6.3% interest. Find how many years it will take for the $5000 to grow to at least $11,000 if interest is compounded
a. quarterly. (Be careful; interest is added to the account only every quarter. See Example.)
b. continuously.
Interest
Meghan Moreau has received a bonus of $25,000. She invests it in an account earning 7.2% compounded quarterly. Find how long it will take for her $25,000 investment to grow to $40,000.
SOLUTION Here P = $25,000, r = 0.072, and m = 4. We also know the amount she wishes to end up with, A = $40,000. Substitute these values into the compound interest formula and solve for time, t.
Note that the interest is calculated quarterly and is added only at the end of each quarter. Therefore, we need to round up to the nearest quarter. She will have $40,000 in 6.75 years.
CAUTION When calculating the time it takes for an investment to grow, take into account that interest is added only at the end of each compounding period. In Example, interest is added quarterly. At the end of the second quarter of the sixth year (t = 6.5), she will have only $39,754.13, but at the end of the third quarter of that year (t = 6.75), she will have $40,469.70.
If A, the amount of money we wish to end up with, is given as well as r, m, and t, then P can be found using the formula for compounded interest. Here P is the amount that should be deposited today to produce A dollars in t years. The amount P is called the present value of A dollars.
Questions & Answers
QUESTION:
Problem 22A
Interest Greg Tobin wishes to invest a $5000 bonus check into a savings account that pays 6.3% interest. Find how many years it will take for the $5000 to grow to at least $11,000 if interest is compounded
a. quarterly. (Be careful; interest is added to the account only every quarter. See Example.)
b. continuously.
Interest
Meghan Moreau has received a bonus of $25,000. She invests it in an account earning 7.2% compounded quarterly. Find how long it will take for her $25,000 investment to grow to $40,000.
SOLUTION Here P = $25,000, r = 0.072, and m = 4. We also know the amount she wishes to end up with, A = $40,000. Substitute these values into the compound interest formula and solve for time, t.
Note that the interest is calculated quarterly and is added only at the end of each quarter. Therefore, we need to round up to the nearest quarter. She will have $40,000 in 6.75 years.
CAUTION When calculating the time it takes for an investment to grow, take into account that interest is added only at the end of each compounding period. In Example, interest is added quarterly. At the end of the second quarter of the sixth year (t = 6.5), she will have only $39,754.13, but at the end of the third quarter of that year (t = 6.75), she will have $40,469.70.
If A, the amount of money we wish to end up with, is given as well as r, m, and t, then P can be found using the formula for compounded interest. Here P is the amount that should be deposited today to produce A dollars in t years. The amount P is called the present value of A dollars.
ANSWER:
Solution:
Step 1 of 2
Given that , and
(a). Here the interest is compounded quarterly
We need to use formula
Since the interest is added at the end of quarter
Hence the required years will be