Accounting Financial Accounting, Spiceland - Downloadable Solutions Manual (Revised)

Appendix C
Time Value of Money



review Questions
Question C-1 (LO C-1) Interest is the cost of borrowing money. Simple
interest is interest we earn on the initial investment only.
Compound interest is the interest we earn on the initial investment plus previous interest. We use
compound interest in calculating the time value of money.

Question C-2 (LO C-2)
To compute a future value, you need to know three amounts: (1) initial investment, (2) the interest
rate per period and (3) the number of periods.

Question C-3 (LO C-2)
Present value tells us the value today of receiving some larger amount in the future. The discount
rate is the rate at which we would be willing to give up current dollars for future dollars.


Question C-4 (LO C-3)
Annuities represent cash payments of equal amounts over equal time intervals.

Question C-5 (LO C-3)
The present value of an annuity is the sum of the present values of a series of cash payments.
BRIEF Exercises


Brief Exercise C-1 (LO C-1)
Oprah should choose the second option, the investment on which interest is
compounded semiannually. The more frequent the rate of compounding, the more
interest we earn on previous interest, resulting in a higher future value.



Brief Exercise C-2 (LO C-2)
Initial Annual Interest Period Future
investment rate compounded invested Value
$15,000 9% Annually 6 years $25,156.50a
a
$15,000 × Future value of $1; n = 6; i = 9%

,Dusty will have enough to buy a car with the Turbo engine.



Brief Exercise C-3 (LO C-2)
Initial Annual Interest Period Future
investment rate compounded invested Value
$27,000 7% Annually 2 years $30,912.30a
a
$27,000 × Future value of $1; n = 2; i = 7%
Arnold and Helene will not be able to pay for their trip.



Brief Exercise C-4 (LO C-2)
Initial Annual Interest Period Future
investment rate compounded invested Value
1. $8,000 10% Annually 7 years $15,589.74a
2. 6,000 12 Semiannually 4 years 9,563.09b
3. 9,000 8 Quarterly 3 years 11,414.18c
a
$8,000 × Future value of $1; n = 7; i = 10%
b
$6,000 × Future value of $1; n = 8; i = 6%
c
$9,000 × Future value of $1; n = 12; i = 2%

Brief Exercise C-5 (LO C-2)
Future Annual Interest Period Present
value Rate compounded invested Value
$6,000 8% Annually 5 years $4,083.50a
a
$6,000 × Present value of $1; n = 5; i = 8%



Brief Exercise C-6 (LO C-2)
Future Annual Interest Period Present
value Rate compounded invested Value

, $55,000 6% Annually 3 years $46,179.06a
a
$55,000 × Present value of $1; n = 3; i = 6%



Brief Exercise C-7 (LO C-2)
Future Annual Interest Period Present
value Rate compounded invested value
1. $10,000 6% Annually 5 years $7,472.58a
2. 7,000 8 Semiannually 8 years 3,737.36b
3. 6,000 12 Quarterly 4 years 3,739.00c
a
$10,000 × Present value of $1; n = 5; i = 6%
b
$7,000 × Present value of $1; n = 16; i = 4%
c
$6,000 × Present value of $1; n = 16; i = 3%




Brief ExerciseAnnual
Annuity C-8 (LO C-3)Interest Period Future value
payment Rate compounded invested of annuity
$4,000 8% Annually 7 years $35,691.21a
a
$4,000 × Future value of annuity; n = 7; i = 8%

Tom and Suri will reach their goal.



Brief Exercise C-9 (LO C-3)
Annuity Annual Interest Period Future value
payment Rate compounded invested of annuity
$3,000 10% Semiannually 5 years $37,733.68a
a
$3,000 × Future value of annuity; n = 10; i = 5%

, Brief Exercise C-10 (LO C-3)
Annuity Annual Interest Period Future value
payment Rate compounded invested of annuity
1. $3,000 7% Annually Six years $ 21,459.87a
2. 6,000 8 Semiannually Nine years 153,872.48b
3. 5,000 12 Quarterly Five years 134,351.87c
a
$3,000 × Future value of annuity; n = 6; i = 7%
b
$6,000 × Future value of annuity; n = 18; i = 4%
c
$5,000 × Future value of annuity; n = 20; i = 3%

Brief Exercise C-11 (LO C-3)
Annuity Annual Interest Period Present value
Payment Rate compounded invested of annuity
$8,000 6% Annually Four years $27,720.88a
a
$8,000 × Present value of annuity; n = 4; i = 6%

The four $8,000 payments (a total of $32,000 received) are worth
$27,720.88 today.



Brief Exercise C-12 (LO C-3)
Annuity Annual Interest Period Present value
Payment Rate compounded invested of annuity
$5,000 10% Annually Ten years $30,722.84a
a
$5,000 × Present value of annuity; n = 10; i = 10%

Since the present value of revenue expected to be received ($30,722.84) is
less than the cost today ($35,000), Monroe should not make the purchase.