Using the present value formula

you deposit $12,000 in an account that pays 6.5% interest compounded quarterly.

A. find the future value after one year?

B. Use the future value formula for simple interest to determine the effective annual yield?

A. Pt = Po(1+r)^n,

r = 6.5% / 4 = 1.625% = 0.01625 = Quarterly % rate expressed as adecimal.

n = 4 comp./yr * 1 yr = 4 compounding
periods.

Pt = 12,000(1.01625)^4 = $12,799.22.

B. APY = I/Po.

I=Pt - Po = 12,799.22 - 12,000 = 799.22
= Interest.

APY=(799.22/12000)*100% = 6.66%.=Annual
Percentage Yield.

Formula: APY = (Pt-Po) / Po

To find the future value of the deposit after one year, we can use the formula for compound interest:

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

Where:
A = future value
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

In this case:
P = $12,000
r = 6.5% = 0.065 (decimal form)
n = 4 (compounded quarterly)
t = 1 (one year)

A. Finding the future value after one year:

A = 12,000(1 + 0.065/4)^(4*1)
A = 12,000(1 + 0.01625)^4
A = 12,000(1.01625)^4
A ≈ 12,000(1.066351) [rounded to six decimal places]
A ≈ $12,759.57

So, the future value of the deposit after one year is approximately $12,759.57.

B. To determine the effective annual yield using the future value formula for simple interest, we can rearrange the formula:

A = P(1 + rt)

Where:
A = future value
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
t = number of years

In this case:
P = $12,000
r = 6.5% = 0.065 (decimal form)
t = 1 (one year)

We can substitute the given values:

$12,759.57 = 12,000(1 + 0.065 * 1)

Now rearrange and solve for the annual interest rate (r):

1 + 0.065 * 1 = (12,759.57 / 12,000)
1 + 0.065 = 1.0632975

0.065 = 1.0632975 - 1
0.065 ≈ 0.0632975

Therefore, the effective annual yield for the deposit is approximately 6.33%.

To solve this problem, we can use the present value formula and the future value formula.

A. To find the future value after one year, we can use the future value formula:

Future Value = Present Value * (1 + (r / n))^(n * t)

Where:
- Present Value = $12,000
- r = interest rate, which is 6.5% or 0.065
- n = number of compounding periods per year, which is 4 (quarterly)
- t = number of years, which is 1 (one year)

Substituting the values into the formula:

Future Value = $12,000 * (1 + (0.065 / 4))^(4 * 1)

Calculating the inside of the brackets:

Future Value = $12,000 * (1 + 0.01625)^(4)

Calculating the exponent:

Future Value = $12,000 * (1.01625)^(4)

Evaluating the exponent:

Future Value = $12,000 * (1.06616171875)

Calculating the final result:

Future Value = $12,793.94

Therefore, the future value after one year will be approximately $12,793.94.

B. To determine the effective annual yield using the future value formula for simple interest, we can rearrange the formula as follows:

Effective Annual Yield = ((Future Value / Present Value) - 1) * 100

Substituting the values:

Effective Annual Yield = (($12,793.94 / $12,000) - 1) * 100

Calculating the division:

Effective Annual Yield = (1.06616171875 - 1) * 100

Calculating the subtraction:

Effective Annual Yield = 0.06616171875 * 100

Calculating the multiplication:

Effective Annual Yield = 6.616171875

Therefore, the effective annual yield is approximately 6.6162%.