Find the value and interest earned if $8906.54 is invested for 9 years at % compounded a) semiannually b) continuosly

Question
Modeling data distributions
asked 2020-11-29
Find the value and interest earned if $8906.54 is invested for 9 years at \(\%\) compounded
a) semiannually
b) continuosly

Answers (1)

2020-11-30
a) The future value for the amount $8906.54 for 9years at \(3\%\) compounded semiannually is calculated a follows.
\(\displaystyle{A}={P}{\left({1}+\frac{r}{{2}}\right)}^{2}{t}{\left(\text{semiannually}\right)}\)
\(\displaystyle{A}={8906.4}{\left({1}+\frac{0.03}{{2}}\right)}^{{{\left({2}\cdot{9}\right)}}}\)
\(\displaystyle=\${11643.88}\)
b) The future value for the amount $8906.54 for 9years at \(3\%\) compounded continuously is calculated a follows.
Future value \(\displaystyle={A}{e}^{r}{t}\)
\(\displaystyle={\left({8906.54}\right)}{e}^{{{\left({0.03}\right)}{\left({9}\right)}}}\)
\(\displaystyle=\${11667.25}\)
Interest earned \(\displaystyle={A}-{P}\)
\(\displaystyle={11667.25}-{8906.54}\)
\(\displaystyle=\${2760.71}\)
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\(\displaystyle​\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) and for 35
\(\displaystyle​\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)
The mileage for the tire pressure \(\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\) is
The mileage for the tire pressure \(\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}\) in. is
(Round to two decimal places as​ needed.)
(D) Write a brief description of the relationship between tire pressure and mileage.
A. As tire pressure​ increases, mileage decreases to a minimum at a certain tire​ pressure, then begins to increase.
B. As tire pressure​ increases, mileage decreases.
C. As tire pressure​ increases, mileage increases to a maximum at a certain tire​ pressure, then begins to decrease.
D. As tire pressure​ increases, mileage increases.
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