Question

Rachel invests $1,000 in a bank account that pays 5% annual interest. How much money will Rachel have in 10 years if the interest is compounded annually?

Answer 1

Greetings!

The formula for compound interest is A = P(1+r)^t, where A = total amount, P = principal (initial amount), r = interest rate (in decimal form), and t = time in years. The rate is 5%. 5% is 0.05 in decimal form. 1 + 0.05 is 1.05. 1 is added, because the 1 represents the whole amount and the amount of money in the account grows. t = 10. Using a calculator, raise 1.05^10. You should get the long decimal 1.62889462678. Do not delete it from the calculator. Multiply it by 1,000 to find the new amount. You get 1,628.89462678 or 1,628.89 when rounded to the nearest hundredth. There. Rachel will have $1,628.89 in her bank account after 10 years.

Answer 2

The compound interest annually will be $1628.90.

Compound interest annually

The question is related to compound interest.

The formula to apply here is;

$A=P\left(1+\frac{r}{n}\right)^{n t}$

where,

• P = principal /beginning amount
• r = interest rate as a decimal
• n = number of compounding's a year
• t = total number of years

If compounded annually, n=1

$p=\ 1000$

$r=5 \%=0.05 t=10$

Amount will be;

$A=1000\left(1+\frac{0.05}{1}\right)^{10}$

$A=1000(1.05)^{10}$

$A=1000 * 1.6289=1628.90$

Amount = $1628.90

Therefore, the compound interest annually will be $1628.90.

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