You need $28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.


A. What single payment could be made at the beginning of the first year to achieve this objective?
B. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

Dhd 4*

A. To find the single payment that could be made at the beginning of the first year to achieve the goal of $28,974 at the end of 10 years, you can use the formula for the future value of a lump sum investment:

Future Value = Present Value * (1 + Interest Rate) ^ Number of Periods

In this case, the present value (the single payment at the beginning) is what we need to find. Let's call it "X."

So the equation becomes:

$28,974 = X * (1 + 0.08) ^ 10

To solve for X, first raise (1 + 0.08) to the power of 10, and then divide $28,974 by that result to find X:

X = $28,974 / (1 + 0.08) ^ 10

X = $28,974 / 1.08 ^ 10

Using a calculator, you can compute the value of X, which is approximately $11,694.47. Therefore, a single payment of $11,694.47 at the beginning of the first year would achieve the objective of having $28,974 at the end of 10 years.

B. To find the amount that could be paid at the end of each year for 10 years to achieve the goal of $28,974, you can use the formula for the future value of an ordinary annuity:

Future Value = Payment * ((1 + Interest Rate) ^ Number of Periods - 1) / Interest Rate

In this case, the future value is $28,974, the interest rate is 8%, and the number of periods is 10.

So the equation becomes:

$28,974 = Payment * ((1 + 0.08) ^ 10 - 1) / 0.08

Now, solve for Payment by multiplying both sides of the equation by 0.08 and then dividing by ((1 + 0.08) ^ 10 - 1):

Payment = $28,974 * 0.08 / ((1 + 0.08) ^ 10 - 1)

Using a calculator, you can compute the value of Payment, which is approximately $2,053.88. Therefore, an amount of approximately $2,053.88 could be paid at the end of each year for 10 years to achieve the objective of having $28,974 at the end of those 10 years.