Answered

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A person invests 3000 dollars in a bank. The bank pays 6.75% interest compounded

semi-annually. To the nearest tenth of a year, how long must the person leave the

money in the bank until it reaches 6700 dollars?

Sagot :

lublana

Answer:

12.1 years

Step-by-step explanation:

We are given that

Principal amount, P=$3000

Rate of interest, r=6.75%  semi-annually

Amount, A=$6700

We know that

When r pays semi-annually

[tex]A=P(1+\frac{r}{n\times 100})^{nt}[/tex]

Where n=2

Using the formula

[tex]6700=3000(1+\frac{6.75}{200})^{2t}[/tex]

[tex]\frac{6700}{3000}=(1..03375)^{2t}[/tex]

[tex]2.233=(1.03375)^{2t}[/tex]

Taking ln on both sides we get

[tex]ln(2.233)=2t ln(1.03375)[/tex]

[tex]2t=\frac{ln(2.233)}{ln(1.03375)}[/tex]

[tex]t=\frac{1}{2}\times \frac{ln(2.233)}{ln(1.03375)}[/tex]

[tex]t=12.1 years[/tex]

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