Question 37921
Suppose you deposit $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer: 
Show work in this space. Use ^ to indicate the power.

A=20,000(1+0.08/1)^(1)=21600 



b) Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.
Answer: 
Show work in this space .

A=20000(1+0.08/4)^4=27209.78 




c) Calculate the return (A) if the bank compounds monthly (n = 12), and carry all calculations to 7 significant figures.
Answer: 
Show work in this space. 

A=20000(1+0.08/12)^12=21659.99

d) Calculate the return (A) if the bank compounds daily (n = 365), and carry all calculations to 7 significant figures.
Answer: 
Show work in this space. 

A=20000(1+0.08/365)^365=21665.55

e) What observation can you make about the increase in your return as your compounding increases more frequently? 
Answer: 

A increases as compounding times increases.

f) If a bank compounds continuous, then the formula becomes simpler, that is 
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. 
Answer: 
Show work in this space 

A=e^(rt)

g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). 
Answer: 
Show work in this space 

25000=20000e^(0.08t)
1.25=e^(0.08t)
Take the natural log of both sides to get:
ln(1.25)=0.08t
0.223/0.08=t
t=2.789



h) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? 
Answer: Show work in this space

40000=20000e^0.08t
2=e^0.08t
Take the natural log of both sides to get:
0.6931...=0.08t
t=8.66 yrs.

Cheers,
Stan H.