## If Jinhee contributes just 5 percent of her salary (\$1850) and earns another \$

If Jinhee contributes just 5 percent of her salary (\$1850) and earns another \$1850 (100 percent)
from her employer%u2019s match she will save a total of \$3700 a year.

%uF0B7 At 8 percent she%u2019d have \$958510.90 = (\$3700 x
259.057 (FVIFA8% 40 years))

%uF0B7 At 10 percent she%u2019d have \$1637594.10 = (\$3700 x 442.593
(FVIFA10% 40 years)).The employer match is
%u201Cfree money%u201D that shouldn%u2019t be passed up. It is in Jinhee%u2019s best interest to start
saving immediately.

Approximately \$2198.49 is required to be saved per year.

Factor Table C solution PV n/a

Calculator solution

PMT (FVIFA6% 3) FV

PV \$0 \$2198.49 PMT ?

3.184 \$7000

I/Y 6% N3
FV \$7000 CPT PMT -\$2198.77

Total interest earned = \$7000 %u2013 (\$2198.77 x 3) = \$403.69
Approximately \$177.95 is required to be saved per month (using a financial calculator).

PV
PMT
I/Y
N
FV
CPT PMT

\$0
? 6%/12=.5% 3*12=36 \$7000 \$177.95

Total interest earned = \$7000 %u2013 (\$177.95 x 36) = \$593.80
By making monthly payments Jinhee will earn \$190.11 (\$593.80 %u2013 \$403.69) more interest.

3. The value of Jinhee%u2019s trust fund value at age 60 is approximately \$190300.

Factor Table C solution PV \$25000 PMT n/a (FVIF7% 30) 7.612

Calculator solution
PV -\$25000 PMT 0
I/Y 7%

29

N 30 FV \$190300 FV ?

CPT FV \$190306.38 4. Paul%u2019s annual payment would be approximately \$12950.

Factor Table D solution

Calculator solution
PV \$100000 PMT ?
I/Y 5%
N 10
FV 0
CPT PMT -\$12950.46

PV PMT

(FVIF5% 10)
FV n/a

\$100000 \$12950

7.722

Paul%u2019s monthly payment would be approximately \$1060.66 (using a financial
calculator).

PV
PMT
I/Y
N
FV
CPT PMT

\$100000
? 5%/12=.4167% 10*12=120

0 -\$1060.66

Paying the loan on a monthly basis would result in an interest savings of \$2225.40 [(\$12950.46 x 10) %u2013 (\$1060.66 x 120)] over the life of the loan.

5. Student answers will vary but these are representative:

%uF0B7 %u201CMax out%u201D tax-deferred savings in employer plans.

%uF0B7 Increase interest rate earned on investments.

%uF0B7 Repay high interest debt as soon as possible.

%uF0B7 Shop for a low-rate mortgage.

DISCUSSION CASE 2 ANSWERS (using a financial calculator)

1. The approximate monthly payment using the calculator is \$2147.29.

PV
PMT
I/Y
N
FV
CPT PMT

-\$400000
? 5%/12=.4167% 30*12=360

0 \$2147.29

2. His retirement income will last for 195 months (16.3 years) or until approximately age 73. His portfolio needs to generate
\$3000 in income per month (\$5800 %u2013 \$2800 retirement annuity).

PV -\$400000 PMT \$3000
I/Y 5%/12=.4167% N?
FV 0
CPT N %uF0BB 195 months

Now his retirement income will last for 945 months (78.8 years) or until approximately age 135. His portfolio only needs to cover
\$1700 per month (\$4500 %u2013 \$2800).

PV -\$400000 PMT \$1700 I/Y 5% N?

FV 0
CPT N %uF0BB 945 months

3. Factoring in the Social Security benefit and using his current projected expense level of \$5800 he will deplete his portfolio
at age 80.

Step 1: The value of the portfolio remaining at age 67 is \$165992.44

Step 2: Using the future value from aboveportfolio will last an additional 156 months or 13
years.

PV PMT I/Y
N
FV CPT FV

-\$400000 \$3000 5%/12=.4167% 11*12=132

? \$165992.44

PV -\$165992.44 PMT \$1450
I/Y 5%/12=.4167% N?

FV 0
CPT N %uF0BB 156 months

4. Yes prices will double by the time he is 80 years old. Using the Rule of 72 you determine that at 3% inflation it takes 24
years for prices to double. The can of soda will cost \$2.43 in 30 years assuming 3% annual inflation.

as the new present value calculates that Doug%u2019s

Factor Table A solution PV \$1 PMT n/a

(FVIF3%30) 2.427 FV \$2.43

Calculator solution PV -\$1 PMT 0
I/Y 3% N 30 FV ? CPT FV \$2.43