Question

Sherman deposited $100 into a bank that offers 3.7% interest rate, compounded daily. In how many years will his balance be $200?

Answer 1

The answer to this is 18.6 years! This is correct on apex

Answer 2

In two years the balance will become $200.

What is compound interest?

Compound interest, also called "compounding interest," is the interest on the initial investment as well as the accrued interest on that investment. Compound interest, which is thought to have started in Italy in the 17th century, can be considered "interest on interest."

What is the formula for compound interest?

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

Where,

A is the final amount

P is the intial prinicpal balance

r is the interest rate

n is number of times interest applied per time period

t is the number of time periods elapsed

According to the given question.

Principal value, P = $100

Interest rate, r = 3.7%

number of times interest, n = 365

Number of time periods elapsed, t = ? ( we have to find)

Amount, A = $200

Now, according to the compound interest formula, we can say that

$A = 100(1+\frac{3.7}{100}) ^{365t}$

$\implies 200 = 100(1+\frac{3.7}{100\times 365}) ^{365t}$

$\implies 2 = (1+ \frac{3.7}{36500}) ^{365t}$

$\implies 2 = (1+0.0001)^{365t}$

$\implies 2 = (1.0001)^{365t}$

Taking log both the sides

$log 2 = 365t log (1.0001)$

$\implies 0.30 = 365t (0.00043)$

$\implies \frac{0.30}{0.00043} = 365t$

$\implies 697.67 = 365t$

$\implies t =\frac{697.67}{365}$

$\implies t = 1.9$

$\implies t = 2$ years

Hence, in two years the balance will become $200.

Find out more information about compound interest here:

https://brainly.com/question/14295570

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