Find the future values of these ordinary annuities. compounding occurs once a year. round your answers to the nearest cent. rework previous parts assuming that they are annuities due. round your answers to the nearest cent.$200 per year for 12 years at 10%.$100 per year for 6 years at 5%.$600 per year for 10 years at 0%.$200 per year for 12 years at 10%.$100 per year for 6 years at 5%.$600 per year for 10 years at 0%

a. $ 4,276.86

b. $ 680.19

c. $ 6,000

d. $ 4,704.55

e. $ 714.20

f. $ 6,000

Step-by-step explanation:

The following formula applies to the first two items:

Where:

P = Periodic payment.

r = rate per period.

n = number of periods.

a. $ 200 per year for 12 years at 10%.

In this case: P = $200, r = 10% or 0.1, and n = 12

We replace in the FV formula:

b. $100 per year for 6 years at 5%.

In this case: P = $100, r = 5% or 0.05, and n = 6.

We replace in the FV formula:

c. $600 per year for 10 years at 0%.

If the interest rate is 0%, simply multiply the amount of money by the number of years during which it will be received.

In this case: P = $600, and n = 10

For the items d. and e., the Future Value of Annuity Due must be applied.

It is the same as saying:

d. $200 per year for 12 years at 10%.

In this case: P = $200, r = 10% or 0.1, n = 12, and FV = 4,276.86 (We obtained this in a. ).

We replace in the FVAD formula:

FVAD = 4,704.546 or (rounded) 4,704.55

e. $100 per year for 6 years at 5%.

In this case: P = $100, r = 5% or 0.05, n = 6, and FV = 680.2 (We obtained this in b. ).

We replace in the FVAD formula:

FVAD = 714.1995 or (rounded) 714.20.

f. $600 per year for 10 years at 0%

Because the interest rate is 0, the ordinary annuity is exactly the same as the due one, that is, $ 6,000.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

the answer will be the last one