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Suppose that
$12,000 is invested in a bond fund and the account grows to
$14,309.26 in 4 yrs.
a. Use the model
A=Pe^(rt) to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.
b. How long will it take the investment to reach
$20,000 if the rate of return continues? Round to the nearest tenth of a year.

Suppose that $\$ 12,000$ is invested in a bond fund and the account grows to $\$ 14,309.26$ in $4$ yrs. $\newline$ a. Use the model $A=P e^{r t}$ to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. $\newline$ b. How long will it take the investment to reach $\$ 20,000$ if the rate of return continues? Round to the nearest tenth of a year.

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Suppose that

\$ 12,000

is invested in a bond fund and the account grows to

\$ 14,309.26

in

4

yrs.

\newline

a. Use the model

A=P e^{r t}

to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.

\newline

b. How long will it take the investment to reach

\$ 20,000

if the rate of return continues? Round to the nearest tenth of a year.

Calculate left side: Now we calculate the left side of the equation. $\frac{ ext{ extdollar}14,309.26}{ ext{ extdollar}12,000} = 1.192438333$
Take natural logarithm: Next, we take the natural logarithm ( $\ln$ ) of both sides to solve for $4r$ . $\ln(1.192438333) = \ln(e^{4r})$ $\ln(1.192438333) = 4r$
Calculate natural logarithm: We calculate the natural logarithm of $1.192438333$ . $\newline$ $\ln(1.192438333) \approx 0.1772$
Divide to find $r$ : Now we divide by $4$ to find $r$ . $\frac{0.1772}{4} = 0.0443$
Convert to percentage: We convert $r$ to a percentage and round to the nearest tenth of a percent. $\newline$ $0.0443 \times 100 = 4.43\%$ $\newline$ Rounded to the nearest tenth: $4.4\%$
Calculate left side: Now we calculate the left side of the equation. $\frac{ ext{ extdollar}20,000}{ ext{ extdollar}12,000} = 1.666666667$
Take natural logarithm: Next, we take the natural logarithm ( $\ln$ ) of both sides to solve for $0.044t$ . $\newline$ $\ln(1.666666667) = \ln(e^{0.044t})$ $\newline$ $\ln(1.666666667) = 0.044t$
Calculate natural logarithm: We calculate the natural logarithm of $1.666666667$ . $\newline$ $\ln(1.666666667) \approx 0.5108$
Divide to find $t$ : Now we divide by $0.044$ to find $t$ . $\frac{0.5108}{0.044} = 11.6091$

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