Question

1. Christopher wants to invest $6200 in a retirement fund that guarantees a return of 9% annually using continously compounded intrest. How much will he have after 20 years?
a) $6002.82
b) $25164.10
c) $37507.81
d) $556342.35

2. You invest $2,600 into a savings account with a 4.25% annual interest rate that compounds interest quarterly. Determine the balance on the account after 5 years.
a) $3766.54
b) $3211.99
c) $3980.50
d) $4560.60

3. You invest $2,600 into a savings account with a 4.25% annual interest rate that compounds interest quarterly. Determine the balance on the account after 50 years.
a) $21,526.87
b) $22,998.70
c) $20,450.10
d) $24,548.33

4. Stock Texas has a price of $156 per share when Bond Austin has a price of $23 per bond. Use an equation modeling the inverse variation between the stock and bond prices to predit the price of stock Texas when bound austin is worth the following: $68.74
a) $59.33
b) $48.115
c) $57.75
d) $52.20

5. What will be your total investment from an annuity of $500 per year compounded continuously earning 8% for 6 years?

Answer 1

1. Continuously compounded formula is given by:
A=Pe^rt
Thus given:
P=$6200, r=0.09, t=20 years:
A=6200e^(0.09*20)
A=37,507.81

Answer: c] $37507.81

2. Compound interest formula is given by:
A=p(1+r/100n)^(nt)
where: n=number of terms, p=principle, t=time, r=rate 
Plugging the values in the formula we get:
A=2600(1+4.25/4*100)^(4*5)
simplifying this we get:
A=$3211.99

Answer: b)$3211.99

3. Using the formula from (2) we have:
A=P(1+r/100n)^nt
plugging in the values we get:
A=2600(1+4.25/400)^(50*4)
Simplifying the above we get:
A=$21526.87

Answer:
A] $21,526.87

4. The price of stock when the bond is worth $68.74 will be:
let the bond price be B and Stock price be S
thus
S=k/B
where
k is the constant of proportionality
thus
k=SB
hence
when S=$156 and B=$23
then
K=156*23
K=3588
thus
S=3588/B
hence
the value of S when B=$68.74
thus
S=3588/68.74
B=52.19668~52.20

Answer: d] $52.20

5. Continuously compounded annuity is given by:

FV =CF×[(e^rt-1)/(e^r-1)]
plugging in the values we get:
FV=500×[(e^(6*0.08)-1)/(e^0.06-1)]
simplifying this we get:
FV=$3698.50