1. How much should be invested now at 5.5% simple interest if $8658 is needed in
ID: 2810705 • Letter: 1
Question
1. How much should be invested now at 5.5% simple interest if $8658 is needed in 2 years?
2. Determine the amount due on the compound interest loan. (Round your answers to the nearest cent.)
$19,000 at 4% for 10 years if the interest is compounded quarterly.
3. Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your answers to two decimal places.)
7.4% compounded weekly.
4. In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.
Find the accumulated amount of the annuity. (Round your answer to the nearest cent.)
$3500 annually at 6% for 10 years.
Explanation / Answer
Question No. 1
Present value = FV / (1 + r)n
Where
FV - future value = 8658
r - rate = 5.5%
n - number of periods = 2
PV = 8658 / (1 + .055)^2
= 7778.80
Question No. 2
Compound interest = P (1 + i)n
Where
P - Principal = 19000
i - nominal annual interest rate in percentage terms = 1% (4%/4)
n - number of compounding periods = 40 (10*4)
= 19000 (1 + .01)^40
= 28288.41
Question No. 3
Years required to double investment = 72/ compound annual interst rate
Effective annual interest rate = (1+(i/n))^n-1
where
i - stated annual interest rate = 7.4%
n - no of compounding periods = 52
Effective annual interest rate = (1+(0.074/52))^52-1
= 7.675%
Years required to double investment = 72/ 7.675
= 9.38
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