Tutorial 1If you get a positive value times a number, You need to shift the decimal to the right as many times as the number specified. If negative, move it to the right.
Simple interest formula = S = FV = P(1 + iK)
Compound interest formula = Sk = P(1 + i)^k
Sn = P(1 + I/T)^n
where I is interest
T is frequency of compounding per year
K is the number of years
N is the total number of periods - K T or TK
Depreciation Formula = Vo or P = Initial value,
Vk = P(1 - d)^k | Tutorial 21. 5 years 1 + r = (FV/PV)^(1/5)
(i) r = 10.38%
(ii) r = 10.47%
(iii) r = 10.51%
(iv) r = 10.52%
(v) r = 10.52%
2. 1 + r = (1 + 0.06/12)^8 ∙ (1 + 0.072/12)^4
1 + r = (1.005)^8 ∙ (1.006)^4
1 + r = (1.0407) ∙ (1.0242) = 1.06591
r = 6.59%
For an initial outlay of $1000, the net return is 1,000(1.067) – 10 = 1,057.
Rate of return 5.7%
For larger outlays, e.g., $10,000, 10,000(1.067) – 10 = 10,660.
Rate of return 6.6%
3. 2500 = 97(1 + r)^40. Take logs of both sides.
Ln(2500/97) = 40Ln(1 + r), or 3.249335 = 40Ln(1 + r), or Ln(1 + r) = 0.0812334
Take the exponential of both sides: 1 + r = 1.084624 and r = 8.4624%
97(1.0867)^40 = 97(27.822) = 2698.72
Either (i) the rate of return is less than the bond rate or (ii) the $97 would have grown to more than $2,500; hence the purchase wasn’t a good investment.
4. (i) 10,000
(ii) 10,000(1.08)^-2 = 10,000(0.8573) = 8573.39
(iii) 10,000(1.08)^-10 = 10,000(0.4632) = 4631.93
5. (i) 1,050(1.05)^-1 = 1000
(ii) 1,108(1.05)^-2 = 1004.99 (*)
(iii) 1,160(1.05)^-3 = 1002.05
6. PV = 10,000(1.07)^-2 + 5,000(1.07)^-3 + 15,000(1.07)^-5
PV = 8,734.39 + 4,081.49 + 10,694.79
PV = 23,510.67
7. 100,000(1 + i)^16 = 125,000
4
(1 + i)^16 = 1.25 → 1 + i = (1.25)^(1/16) = 1.014044
4
i = 0.0562 or 5.62%
OR use logarithms
Ln[(1 + i/4)^16] = Ln 1.25 and 16Ln(1 + i/4) = 0.22314
Ln(1 + i/4) = 0.0139465 and 1 + i/4 = 1.014044.
8. 15,000(1 + 0.055)^(12k) = 30,000
12
(1 + 0.055)^(12k) = 2
12
12k Ln(1 + 0.055) = Ln 2
12
12k 0.0045728 = 0.69315
k = 12.63 years. About 12 years and 7½ months. | Tutorial 3 |
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