 Mathematics
29 March, 16:58

# Alex plans to invest \$6000 for 10 years. Determine how much each investment would be worth to Alex as the CD matures.A. Capitol Banks offers a 10 year CD at an annual rate of 5% using simple interest.B. Charter Banks offers a 10 year CD at annual rate of 4.9% using monthly compound interest.C. State Bank offers a 10 year CD at an annual rate of 4.8 % using continuous compounding.

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1. 29 March, 18:01
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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