Answer:
Step-by-step explanation:
Q1.
Use FV formula to get value at year 7
FV= PV [tex](1+r)^{t}[/tex]
Since it's quarterly compounding, quarterly rate would be (5.5% / 4)= 1.375% and total duration t would be 7*4 = 28 quarters
FV= 4,500 [tex](1+0.01375)^{28} = 4,500 * 1.46576478[/tex]
FV= $6,595.94
Q2.
Future Value with continuous compounding formula; FV= PV[tex]e^{rt}[/tex]
Note: the "e" is an exponential
FV= 3,200[tex]e^{0.0375 * 2}[/tex]
FV = 3200* 1.0778841
FV= $3,440.229
Q3.
Here, you find Present value; PV = [tex]\frac{FV}{(1+r)^{t} }[/tex]
Since it's monthly compounding, monthly rate would be (4.75% / 12)= 0.3958% and total duration t would be 18*12 = 216 months
PV= [tex]\frac{40,000}{(1+0.003958)^{216} }[/tex]
PV= 40,000/2.3472409
PV= 17,041.2845
Therefore you need to invest $17,041.28.
Q4.
Use PV with continuous compounding formula here;
PV= [tex]\frac{FV}{e^{rt} }[/tex]
Note: the "e" is an exponential
PV = [tex]\frac{30,000}{e^{0.0525 * 7} } \\[/tex]
PV= 30,000/1.4441198
PV = $20,773.8998
Therefore, you need to invest $20,773.90 now.
Q5.
Compare the FV of each option and choose the highest;
a.) FV= PV [tex](1+r)^{t}[/tex]
Since it's semi-annual compounding, semi-annual rate would be (5.6% / 2)= 2.8% and total duration t would be 8*2 = 16
FV = 11,500[tex](1+0.028)^{16} = 11,500 * 1.555570987[/tex]
FV= $17,889.07
b.)Future Value with continuous compounding formula; FV= PV[tex]e^{rt}[/tex]
Note: the "e" is an exponential
FV= 11,500[tex]e^{0.0345 * 5}[/tex]
FV= 11,500 * 1.188271821
FV= $13,665.126
Therefore, Option A is a better option by $4,223.94
