Question

Zachary invested $700 in an account paying an interest rate of 4.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,360?

Answer 1

Answer:

14

Step-by-step explanation:

Answer 2

The nearest time period for Zachary to reach the amount is 14 years.

What is compound interest?

Compound interest is the interest on a deposit or loan calculated based on the initial principle, and the collective interest from previous periods.

For the given situation,

Principle, $p=\ 700$

Interest rate, $r=4.9\%$$=0.049$

Amount, $a=\ 1360$

Compounded continuously, $n=1$

We have to find the time period, $t$

The amount formula of compound interest, $a=p(1+\frac{r}{n} )^{nt}$

On substituting the values,

$1360=700(1+\frac{0.049}{1} )^{1t}$

Divide by $700$ on both sides,

⇒$\frac{1360}{700}=\frac{700}{700} (1+0.049 )^{t}$

⇒$1.94=(1.049)^{t}$

Taking log on both sides,

⇒㏒$1.94$=$t$㏒$1.049$

⇒$0.28=0.020t$

Divide by $0.020$ on both sides,

⇒$\frac{0.28}{0.020}=t$

⇒$t=14$

Hence, the time period is 14 years.

Learn more about compound interest here

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