An investment of $8000 grows to $10,292.76 in 4 years. Find the annual rate of return for annual compounding. [Hint: Use P(1 + r/m)^mt with m = 1 and solve for r (rounded to one decimal place).]

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calculista calculista · Answer 1 · 2020-03-01T05:47:05+01:00

Answer:

[tex]r=6.5\%[/tex]

Step-by-step explanation:

we know that

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

[tex]t=4\ years\\ P=\$8,000\\A=\$10,292.76\\r=?\\n=1[/tex]

substitute in the formula above

[tex]10,292.76=8,000(1+\frac{r}{1})^{1*4}[/tex]

solve for r

[tex]10,292.76=8,000(1+r)^{4}[/tex]

[tex](10,292.76/8,000)=(1+r)^{4}[/tex]

Elevated to 1/4 both sides to remove the exponent in the right side

[tex](10,292.76/8,000)^{1/4}=(1+r)[/tex]

[tex]r=(10,292.76/8,000)^{1/4}-1[/tex]

[tex]r=0.065[/tex]

Convert to percentage

[tex]r=6.5\%[/tex]