Question

1. Exercise A3-20 (Algorithmic)
   Future Values of an Annuity

   Use Future Value Tables or your calculator to complete the requirements below.

   On December 31, 2020, you sign a contract to make annual deposits of $5,200 in an investment account that earns 10%. The first deposit is made on December 31, 2020.

   Required:

   1. Calculate what the balance in this investment account will be just after the seventh deposit has been made if interest is compounded annually. Round your answer to the nearest cent, if rounding is required.
   $

   2. Determine how much interest will have been earned on this investment account just after the seventh deposit has been made if interest is compounded annually. Round your answer to the nearest cent, if rounding is required.
   $

2. Exercise A3-11 (Algorithmic)
   Practice with Tables

   Use Future Value Tables and Present Value Tables, or your calculator, to complete the requirements below.

   Required:

   Round your answers to the nearest cent, if rounding is required.

   a. Determine the future value of a single cash flow of $5,480 that earns 7% interest compounded annually for 10 years.
   $

   b. Determine the future value of an annual annuity of 10 cash flows of $500 each that earns 7% compounded annually.
   $

   c. Determine the present value of $5,480 to be received 10 years from now, assuming that the interest (discount) rate is 7% per year.
   $

   d. Determine the present value of an annuity of $500 per year for 10 years for which the interest (discount) rate is 7% per year and the first cash flow occurs one year from now.
   $

   Feedback

3. 12)b. Determine the present value of an annuity of seven cash flows of $1,340 each (one at the end of each of the next 7 years) for which the interest (discount) rate is 8% per year.

Answer 1

A-3) 20) 1) Future value (F. V.) of annual deposits = Annual deposits * ((1 + i)^n - 1) / i)

Here,

i (rate) = 10% or 0.10

n (years) = 7 years

Annual deposits = $5,200

Now,

F. V. Of annual deposits = $5,200 * ((1 + 0.10)^7) - 1) / 0.10)

F. V. Of annual deposits = $5,200 * (0.9487 / 0.10)

F. V. Of annual deposits = $5,200 * 9.4872

F. V of annual deposits = $49,333.29

2) Interest earned = Future value of deposits - Total deposits

Interest earned = $49,333.29 - ($5,200 * 7 years)

Interest earned = $49,333.29 - $36,400

Interest earned = $12,933.29

A-3) 11) a) Future value (F. V.) of deposit = Deposit * (1+i)^n

Here, i (rate) = 7% or 0.07

n (years) = 10

Deposit = $5,480

Now,

F. V. Of deposit = $5,480 * (1 + 0.07)^10

F. V. Of deposit = $5,480 * 1.9672

F. V. Of deposit = $10,779.99

b) F. V. Of annual deposits = Annual deposits * ((1 + i)^n) - 1) / i)

Here, i (rate) = 7% or 0.07

n (years) = 10

Annual deposits = $500

Now,

F. V. Of annual deposits = $500 * ((1 + 0.07)^10) - 1) / 0.07)

F. V. Of annual deposits = $500 * (0.9672 / 0.07)

F. V. Of annual deposits = $500 * 13.8171

F. V. Of annual deposits = $6,908.55

c) Present value of amount = Amount * (1 / (1+i)^n)

Here, Amount = $5,480

i (rate) = 7% or 0.07

n (years) = 10

Now,

Present value of amount = $5,480 * (1 / (1 + 0.07)^10)

Present value of amount = $5,480 * 0.5083

Present value of amount = $2,785.48

d) Present value (P. V.) of annuity = Annual amount * ((1 - (1/(1 + i)^n)) / i)

Here, i (rate) = 7% or 0.07

n (years) = 10

Annual amount = $500

Now,

P. V. Of annuity = $500 * ((1 - (1/(1 + 0.07)^10)) / 0.07)

P. V. Of annuity = $500 * ((1 - 0.5083) / 0.07)

P. V. Of annuity = $500 * 7.0243

P. V. Of annuity = $3,512.15

12) b) P. V. Of annuity = Annual amount * ((1 - (1/(1+i)^n) / i)

Here, i (rate) = 8% or 0.08

n (years) = 7

Annual amount = $1,340

Now,

P. V. Of annuity = $1,340 * ((1 - (1/(1+0.08)^7)) / 0.08)

P. V. Of annuity = $1,340 * ((1 - 0.5835) / 0.08)

P. V. Of annuity = $1,340 * 5.2063

P. V. Of annuity = $6,976.44