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

Rachel will have approximately $1628.89 with annual compounding interest, $1647.01 with monthly compounding interest, and $3678.79 with continuous compounding interest after 10 years.

Step-by-step explanation:

To calculate the amount of money Rachel will have in 10 years with annual compounding interest, we can use the formula: A = P(1 + r/n)^(nt), where A is the amount of money at the end, P is the principal amount (the initial amount of money), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. In this case, Rachel invests $1,000 with an annual interest rate of 5% and we are looking for A after 10 years.

For annual compounding, n is 1. Plugging in the values into the formula:

1. A = 1000(1 + 0.05/1)^(1*10)
2. A = 1000(1 + 0.05)^10
3. A = 1000(1.05)^10
4. A ≈ 1000(1.62889)
5. A ≈ 1628.89

Therefore, Rachel will have approximately $1628.89 in the bank account after 10 years with annual compounding interest.

For monthly compounding, n is 12 (as there are 12 months in a year). Plugging in the values into the formula:

1. A = 1000(1 + 0.05/12)^(12*10)
2. A = 1000(1 + 0.004167)^120
3. A ≈ 1000(1.004167)^120
4. A ≈ 1000(1.64701)
5. A ≈ 1647.01

Therefore, Rachel will have approximately $1647.01 in the bank account after 10 years with monthly compounding interest.

For continuous compounding, we can use the formula: A = Pe^(rt), where e is Euler's number (approximately 2.71828). Plugging in the values into the formula:

1. A = 1000e^(0.05*10)
2. A ≈ 1000(2.71828)^(0.5)
3. A ≈ 1000(3.678794)
4. A ≈ 3678.79

Therefore, Rachel will have approximately $3678.79 in the bank account after 10 years with continuous compounding interest.

Answer 2

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+(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+(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+(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