2 years ago

PLZ HELP ASAPPPP PLEASE

Mathematics

1 answer:

Law Incorporation [45]2 years ago

6 0

Answer:

(-1, -8)

Step-by-step explanation:

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If $5200 is invested at a rate of 8.6% compounded quarterly, how long will it take, to the nearest hundredth of a year, until th

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Answer:

$t= 9.43\ years$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

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

$t=?\ years\\ P=\$5,200\\ r=8.6\%=8.6\100=0.086\\n=4\\A=\$11,600$

substitute in the formula above

$11,600=5,200(1+\frac{0.086}{4})^{4t}$

$11,600=5,200(1.0215)^{4t}$

$(11,600/5,200)=(1.0215)^{4t}$

Applying log both sides

$log(11,600/5,200)=log(1.0215)^{4t}$

applying property of logarithms

$log(11,600/5,200)=(4t)log(1.0215)$

$t=log(11,600/5,200)/[(4)log(1.0215)]$

$t= 9.43\ years$

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