1. Q1 Find the PV of perpetuity, then discount into Year 0 terms
14, / (1.14)^2 = 76,947
𝑃.𝐼.= 76,947 80,000 = .96

2. Q2 Find the EAR that links the two SAR’s
Quarterly rate = =
EAR = −1=
Monthly Rate = −1=
𝑺𝑨𝑹=𝟏𝟐 ∗ .𝟎𝟎𝟔𝟎𝟒= .𝟎𝟕𝟐𝟓𝟔

3. Q3 Simple Interest FV formula: 𝐹𝑉=𝑃𝑉 1+𝑟∗𝑇 𝐹𝑉=4,000 1+.1∗8 =7,200
7,200−4000=3,200

4. Q4
Investment 1: NPV= −50, =4545
Investment 2: NPV= −30, =−909
Investment 3 : First try 50,000 into Investment 3
NPV = −50, ∗ =1652
Investment 1 has higher NPV than 3), so invest 50,000 in 1) and the remaining 30,000 in 3)

5. Q5
Find the PV of monthly perpetuity standing in Month 5 by converting SAR into EAR
Monthly Rate = =
EAR= −1=.20745
𝑃 𝑉 𝑀𝑜𝑛𝑡ℎ5 = =3374
𝑷 𝑽 𝑴𝒐𝒏𝒕𝒉𝟎 = 𝟑𝟑𝟕𝟒 𝟏.𝟎𝟏𝟓𝟖𝟑𝟑 𝟓 =𝟑𝟏𝟏𝟗

6. Q6
Internal rate of return s.t. : −600− 𝑟 𝑟 2 =0 Make: 1+𝑟=𝑥 −600 𝑥 2 −800𝑥+1400=0 3 𝑥 2 +4𝑥−7=0 Use quadratic formula X=1

7. Q7
Equate the two cash flows: 1,000,000= 1000 𝑤𝑒𝑒𝑘𝑙𝑦 𝑟𝑎𝑡𝑒 𝑤𝑒𝑒𝑘𝑙𝑦 𝑟𝑎𝑡𝑒= .001 𝐸𝐴𝑅= −1= .0534

8. Q8 Year 0 – 1 : 500 *(1.09)=545 Year 1 – 2 : (500+545) *(1.09)=1139.05
3 years from today: =2286

9. Q9
𝑟+1= 1+𝑛 1+𝜋
𝑟+1= =.8
r = -.2

10. Q10
130,000=90,000 1+𝑟 32 𝑟=𝑠𝑒𝑚𝑖𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒= SAR= r*2 = .0232

11. Q11
90000=15000∗ 1− 1.14 −𝑡 .14 𝑡= 𝑙𝑜𝑔 6.25 𝑙𝑜𝑔 1.14 =14

12. Q12
90,000 15,000 =6 years

13. Q13
Use the annuity formula to find PV of withdrawals standing in year 17 (which is also balance you need at year 17)
𝑃 𝑉 17 = ∗ 1− −23
Discount back to year 10
𝐷𝑒𝑝𝑜𝑠𝑖 𝑡 𝑌𝑒𝑎𝑟10 ∗ =𝑃 𝑉 17
𝐷𝑒𝑝𝑜𝑠𝑖𝑡= 𝑃 𝑉 ^7 =477,791

14. Q14a Equal deductions of principle: 600 over 6 years
600/6 =100 each year

15. Q14b PV of payments should equal principle 𝑥 1.15 4 + 2𝑥 1.15 7 =600
𝑥 𝑥 =600
Or do it manually
(((600∗1.15^4)-x)*1.15^3)-2x=0
X=453.3
2x=906.6