Question

Alex plans to invest $6000 for 10 years. Determine how much each investment would be worth to Alex as the CD matures.

Answer 1

Answer:

Step-by-step explanation:

A. The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the amount of money deposited.

P represents the principal or amount of money deposited.

R represents interest rate on the deposit.

T represents the duration of the deposit in years.

From the information given,

P = $6000

R = 5%

T = 10 years

Therefore,

I = (6000 × 5 × 10)/100

I = $3000

Total amount = 6000 + 3000 = $9000

B. We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 6000

r = 4.9% = 4.9/100 = 0.049

n = 12 because it was compounded 12 times in a year.

t = 10 years

Therefore,

A = 6000(1 + 0.049/12)^12 × 10

A = 6000(1 + 0.049/12)^120

A = $9780

C. The formula for continuously compounded interest is

A = P x e^(r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

r = 4.8% = 4.8/100 = 0.048

Therefore,

A = 6000 x e^(0.048 x 10)

A = 6000 x e^(0.48)

A = $9696