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3 years ago

Alexandra invested $20,000 in an account paying an interest rate of 6.2%

Mathematics

1 answer:

bazaltina [42]3 years ago

5 0

Answer:

5.1

Step-by-step explanation:

Compounded Annually:

A=P(1+r)^t

A=P(1+r)

A=27200\hspace{35px}P=20000\hspace{35px}r=0.062

A=27200P=20000r=0.062

Given values

27200=

\,\,20000(1+0.062)^{t}

20000(1+0.062)

Plug in values

27200=

\,\,20000(1.062)^{t}

20000(1.062)

Add

\frac{27200}{20000}=

20000

27200

\,\,\frac{20000(1.062)^{t}}{20000}

20000

20000(1.062)

Divide by 20000

1.36=

\,\,1.062^t

1.062

\log\left(1.36\right)=

log(1.36)=

\,\,\log\left(1.062^t\right)

log(1.062

)

Take the log of both sides

\log\left(1.36\right)=

log(1.36)=

\,\,t\log\left(1.062\right)

tlog(1.062)

Bring exponent to the front

\frac{\log\left(1.36\right)}{\log\left(1.062\right)}=

log(1.062)

log(1.36)

\,\,\frac{t\log\left(1.062\right)}{\log\left(1.062\right)}

log(1.062)

tlog(1.062)

Divide both sides by log(1.062)

5.1116317=

\,\,t

Use calculator

t\approx

t≈

\,\,5.1

5.1

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