Respuesta :
Answer:
11.86%
7.13%
19.95%
8.97%
Explanation:
interest rate = [tex]\frac{future value}{present value}}^{\frac{1}{n} } - 1[/tex]
(317/181)^ (1/5) - 1 = 11.86%
1080/335)^(1/17) - 1 = .13%
(185,382/48,000)^(1/13) - 1 = 19.95%
(531,618 / 40,353)^(1/30) - 1 = 8.97%
The interest rate in the 1 case is 5.01%, 2 case is 5.79%, 3 case is 8.05%, 4 case is 10.60%.
What is interest rate?
An interest rate is the amount of interest owed per period, as a quotient of the amount lent, deposited, or borrowed.
Computation of the interest rates :
The formula for future value is:
[tex]\text{FV}= \text{PV} \ (1+r)^n[/tex]
where,
PV=present value
r=interest rate
n =number of periods/ years
FV = future value.
Then, the formula for finding r is :
[tex]\text{FV}= \text{PV} \ (1+r)^n\\\\r= (\dfrac{\text{FV}}{\text{PV}})^\dfrac{1}{\text{n}-1}[/tex]
case1:
put the above formula in case 1 we get:
[tex]r= (\dfrac{\text{\$231}}{\text{\$190}})^\dfrac{1}{4}-1}\\\\r= (\dfrac{\text{\$231}}{\text{\$190}})^{0.25-1}\\\\r=(1.21578947)^{0.25-1}\\\\r=1.05006116 -1\\\\r=0.05006116\times100\\\\r=5.01%[/tex]
case2:
Put the above formula in case 2 we get:
[tex]r= (\dfrac{\text{\$854}}{\text{\$310}})^\dfrac{1}{18}-1}\\\\r= (\dfrac{\text{\$854}}{\text{\$310}})^{0.0555-1}\\\\r=(2.75483871)^{0.0555-1}\\\\r=1.05785304 -1-1\\\\r=0.05785304\times100\\\\r=5.79%.[/tex]
case3:
Put the above formula in case 3 we get:
[tex]r= (\dfrac{\text{\$1,48,042}}{\text{\$34,000}})^\dfrac{1}{19}-1}\\\\r= (\dfrac{\text{\$1,48,042}}{\text{\$34,000}})^{0.0526-1}\\\\r=(4.35417647)^{0.0526-1}\\\\r=1.08045444 -1\\\\r=0.08045444\times100\\\\r=8.05%[/tex]
case4:
Put the above formula in case 4 we get:
[tex]r= (\dfrac{\text{\$412,862}}{\text{\$36,261}})^\dfrac{1}{25}-1}\\\\r= (\dfrac{\text{\$412,862}}{\text{\$36,261}})^{0.04-1}\\\\r=(12.4127958)^{0.04-1}\\\\r=1.10599913 -1\\\\r=0.10599913\times100\\\\r=10.60%.[/tex]
Learn more about interest rate, refer:
https://brainly.com/question/4626564
