Question
Ali received a
bonus. He decided to invest it in a 5 -year certificate of deposit (CD) with an annual interest rate of
compounded quarterly
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Ali’s account
after 5 years?
(b) How much interest is earned on Ali’s investment after 5 years?
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas.
(a) Assuming no withdrawals are made, how much money is in Ali’s account
after 5 years?
(b) How much interest is earned on Ali’s investment after 5 years?
Ask by Pearson Griffin. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After 5 years, Ali has $2256.48 in his account and earns $156.48 in interest.
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Extra Insights
To solve Ali’s investment problem, we will use the formula for compound interest:
where:
-
is the amount of money accumulated after n years, including interest. -
is the principal amount (the initial amount of money). -
is the annual interest rate (decimal). -
is the number of times that interest is compounded per year. -
is the number of years the money is invested for.
Given:
-
-
(which is as a decimal) -
(since interest is compounded quarterly) -
(a) Calculate the total amount after 5 years:
Calculating within the parentheses:
Thus,
Calculating inside the parentheses:
Now, raise it to the power of 20:
Calculating
:
Now calculate
:
So, after 5 years, the amount in Ali’s account is approximately
.
(b) To find out how much interest is earned on Ali’s investment after 5 years, subtract the principal from the total amount:
Thus, the total interest earned is approximately
.
Final answers:
(a)
(b)
(a)
(b)