Problem 1: The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:
A = P[(1 + (r/n)]nt
A is the amount of returned
P is the principal amount deposited
r is the annual interest rate (expressed as a decimal)
n is the compound period
t is the number of years
Carry all calculations to 6 decimals on all assignments then round the answer to the nearest cent.
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).
b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
e) What observation can you make about the size of increase in your return as your compounding increases more frequently?
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. Round your answer to the hundredth's place.