1
a. 25.000 / (1 + 0.04)5 = $20.548,18
b. 25.000 / (1 + 0.06)5 = $18.681,45
c. 25.000 / (1 + 0.08)10 = $11.579,84
2
a. (.04) / 1.045 = $790.31 (.04) / 1.045 = $20.548,18
b. (.06) / 1.065= $1057.44 (.06) / 1.065 = $18.681,45
c. (.08) / 1.0810 = $857.77 (.08) / 1.0810 = $11.579,84
3
a. .04 = $961.54 .04 = $25.000
5
b. ..04 = $790.31 ..045 = $20.548,18
c. .04 (1 – .045) = $171.22 .04 x (1 – (.045 ))= $4451,82
d. Answer a is the highest, because the payments start next year, there is not much benefit from
the interest rate yet. Answer c is much lower than a & b, because it is a lasting stream of cash
flows; an annuity.
Answer c is answer a minus answer b; a perpetuity – a delayed perpetuity
4
Formula: FV = C1 / r x ( (1 + r)t – 1)
1.000.000 = ? / 0.05 x (1.0510 – 1)
? = 1.000.000 / (1.0510 – 1) x 0.05 = $79.504,57
Each year you have to put aside $79.504,57 to become a millionaire.
5
FV = C1 / r x ( (1 + r)t – 1)
FV (68 years) = .05 x (1.0530 – 1) = €332.194,24 at retirement
If he wants the funds to last until he is 90:
€332.194,24 = C.05 x (1 – 1 / (1.05)21) C1 = €25.909,86 each year
If he assumes he’ll live forever:
C1 = 332.194,24 x 0.05 = €16.609,71 each year
6
a. PV = C1 / r x (1 – 1 / (1 + r)t )= .0025 x (1 – .002524) = €1349,43
b. PV = 977 + ,025 x (1 – .0025 24) = €1512,12
Which means you should take option 1, because it will cost you less money.
a. 25.000 / (1 + 0.04)5 = $20.548,18
b. 25.000 / (1 + 0.06)5 = $18.681,45
c. 25.000 / (1 + 0.08)10 = $11.579,84
2
a. (.04) / 1.045 = $790.31 (.04) / 1.045 = $20.548,18
b. (.06) / 1.065= $1057.44 (.06) / 1.065 = $18.681,45
c. (.08) / 1.0810 = $857.77 (.08) / 1.0810 = $11.579,84
3
a. .04 = $961.54 .04 = $25.000
5
b. ..04 = $790.31 ..045 = $20.548,18
c. .04 (1 – .045) = $171.22 .04 x (1 – (.045 ))= $4451,82
d. Answer a is the highest, because the payments start next year, there is not much benefit from
the interest rate yet. Answer c is much lower than a & b, because it is a lasting stream of cash
flows; an annuity.
Answer c is answer a minus answer b; a perpetuity – a delayed perpetuity
4
Formula: FV = C1 / r x ( (1 + r)t – 1)
1.000.000 = ? / 0.05 x (1.0510 – 1)
? = 1.000.000 / (1.0510 – 1) x 0.05 = $79.504,57
Each year you have to put aside $79.504,57 to become a millionaire.
5
FV = C1 / r x ( (1 + r)t – 1)
FV (68 years) = .05 x (1.0530 – 1) = €332.194,24 at retirement
If he wants the funds to last until he is 90:
€332.194,24 = C.05 x (1 – 1 / (1.05)21) C1 = €25.909,86 each year
If he assumes he’ll live forever:
C1 = 332.194,24 x 0.05 = €16.609,71 each year
6
a. PV = C1 / r x (1 – 1 / (1 + r)t )= .0025 x (1 – .002524) = €1349,43
b. PV = 977 + ,025 x (1 – .0025 24) = €1512,12
Which means you should take option 1, because it will cost you less money.
