A bank offers an investment account with an annual interest rate of
1.46%
compounded daily. Diane invests
$4300
into the account for
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. Assume there are
365
days in each year.
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To calculate the final amount in Diane’s investment account after 5 years and the interest earned, we can use the compound interest formula. In this case, the interest is compounded daily, and we’ll assume there are 365 days in each year. The compound interest formula is as follows:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
(a) Finding the final amount after 5 years:
Diane’s initial investment (P) is $4,300.
The annual interest rate (r) is 1.46%, which is 0.0146 as a decimal.
The interest is compounded daily, so n = 365 (number of compounding periods per year).
The investment is held for 5 years (t = 5).
Now, we can plug these values into the formula:
A = 4300 * (1 + 0.0146/365)^(365*5)
A = 4300 * (1 + 0.000040)^(1825)
A ≈ 4300 * 1.073498
A ≈ $4,621.09
So, after 5 years, there will be approximately $4,621.09 in Diane’s account.
(b) Calculating the interest earned:
To find the interest earned, we need to subtract the initial investment (P) from the final amount (A):
Interest = A – P
Interest = $4,621.09 – $4,300
Interest ≈ $321.09
Diane will earn approximately $321.09 in interest on her investment after 5 years.
In summary, after 5 years of investing $4,300 at an annual interest rate of 1.46% compounded daily, Diane will have approximately $4,621.09 in her account, and she will earn approximately $321.09 in interest.
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