Question

MAJORR HELP!!!
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?
How much money will Rachel have in 10 years if the interest is compounded monthly?
How much money will Rachel have in 10 years if the interest is compounded continuously?

Answer 1

Answer:

a)$1628.90

b)$1647.00

c)$1648.72

Step-by-step explanation:

The question is on compound interest.

The formula to apply here is;

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

where

• P=principal /beginning amount
• r=interest rate as a decimal
• n=number of compoundings a year
• t=total number of years

a) If compounded annually, n=1

p=$1000, r=5%=0.05 t=10

Amount will be;

$A=1000(1+\frac{0.05}{1} )^{10} \\\\\\A=1000(1.05)^{10} \\\\\\A=1000*1.6289=1628.90$

Amount=$1628.90

b) If compounded monthly, n=12

p=$1000, r=5%=0.05, t=10, n=12

$A=1000(1+\frac{0.05}{12} )^{12*10} \\\\\\A=1000(1.0042)^{120} \\\\\\A=1000*1.647=1647$

Amount=$1647.00

c)If interest compounded continuously, it means the principal is earning interest constantly and the interest keeps earning on the interest earned.Here the formula to apply is;

A=Pe^rt where e is the mathematical constant e=2.71828182846

Hence the amount will be;

$A=Pe^{rt} \\\\\\A=1000*e^{0.05*10} \\\\\\A=1000*2.71828182846^{0.5} \\\\\\A=1648.72$

Amount=$1648.72