Question

Ch. 6 Time Value of Money Concepts (2 marks) E6-6 Present value; annuities Using the appropriate present value table and assuming a 12% annual interest rate, determine the present value on December 31, 2013, of a five-period annual annuity of $5,000 under each of the following situations: 1. The first payment is received on December 31, 2014, and interest is compounded annually. 2. The first payment is received on December 31, 2013, and interest is compoundled annually. 3. The first payment is received on December 31, 2013, and interest is compounded quarterly. LO7 E6-7 Solving for For each of the following situations involving single amounts, solve for the unknown (?). Assume that interest is compounded annually. (i = interest rate, and n = number of years) unknowns; single amounts Present Value n L04 Future Value $ 40,000 65,000 40,000 100,000 ? $36,289 15,884 46,651 15,376 i 10% ? 8 ? 7 3. 4 5 10 ? 8 20

Answer 1

SOLUTION:

E6-6:

Using the appropriate present value table and assuming a 12% annual interest rate, determine the present value on December 31, 2016, of a five-period annual annuity of S5,000 under each of the following situations:

1. The first payment is received on December 31, 2014, and interest is compounded annually.

The present value of an ordinary annuity of $1 factor where n = 5 years, i = 12% is 3.60478 * $5,000 = $18023.9

2. The first payment is received on December 31, 2013, and interest is compounded annually.

The present value of an annuity due of $1 factor where n = 5 years, i = 12% is 4.03735 * $5,000 = $20,186.75

3. The first payment is received on December 31, 2013, and interest is compounded quarterly

The present value of an annuity due of $1 factor where n = 5 years, i = 12% is 14.8773 * $5,000 = $74,386.5

E6-7:

Case 1

The equation for the present value (P) and the future value (F) can be expressed as shown below:

F = (1 + i) ^{n} * P

$40,000=(1+10%)5*P

On solving the above equation we get, P = $24,836.85

Case 2

The equation for the present value (P) and the future value (F) can be expressed as shown below:

F = (1 + i) ^{n} * P

$65,000=(1+i)10∗$36,289

On solving the above equation we get, i = 6%

Case 3

The equation for the present value (P) and the future value (F) can be expressed as shown below:

F = (1 + i) ^{n} * P

$40,000=(1+8%)n∗15,884

On solving the above equation we get, n = 12

Case 4

The equation for the present value (P) and the future value (F) can be expressed as shown below:

F = (1 + i) ^{n} * P

$100,000=(1+i)8∗$46,651

On solving the above equation we get, i = 10%

Case 5

The equation for the present value (P) and the future value (F) can be expressed as shown below:

F = (1 + i) ^{n} * P

F=(1+7%)20∗$15,376

On solving the above equation we get, F = $59,489.74