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Use the compound interest formula A(t)=P(1+ \frac{r}{n})^{nt} and round to the hundredths place, if necessary. Do not include commas in your answers.An account is opened with an initial deposit of$6500 and earns 3.6% interest compounded semi-annually. What will the account be worth in 20 years? AnswerHow much would the account have been worth if the interest were compounding weekly? Answer

Use The Compound Interest Formula AtP1 Fracrnnt And Round To The Hundredths Place If Necessary Do Not Include Commas In Your AnswersAn Account Is Opened With An class=

Sagot :

We need to use the formula:

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

to find the worth of the account in 20 years.

We know that:

[tex]\begin{gathered} P=6500 \\ r=3.6\%=0.036 \\ n=2 \\ t=20 \end{gathered}[/tex]

Thus, we obtain:

[tex]\begin{gathered} A(20)=6500\cdot(1+\frac{0.036}{2})^{2\cdot20} \\ \\ A(20)=6500\cdot(1+0.018)^{40} \\ \\ A(20)=6500\cdot(1.018)^{40} \\ \\ A(20)=13268.58 \end{gathered}[/tex]

Therefore, the account, after 20 years, will be worth $13268.58.

If the interest were compounded weekly, n would be:

[tex]n=\frac{365}{7}\cong52[/tex]

Then, the account would have been worth:

[tex]\begin{gathered} A(20)=6500\cdot(1+\frac{0.036}{52})^{52\cdot20} \\ \\ A(20)=6500\cdot(1+\frac{0.036}{52})^{1040} \\ \\ A(20)\cong13350.49 \end{gathered}[/tex]

Notice that if we do not approximate the number of weeks (n) to 52, and instead use its exact value (365/7), then we obtain:

[tex]A(20)=6500\cdot\mleft(1+\frac{0.036}{\frac{365}{7}}\mright)^{\frac{365}{7}\cdot20}\cong13350.50[/tex]

If the interest were compounded weekly, the account would have been worth $13350.49 (using n = 52).

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