Help Help Help?

Question

The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by
A=P (1+r/n)
A is the amount of returned.
P is the principal amount initially 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 $10,000 for 2 years at a rate of 10%.

a) Calculate the return (A) if the bank compounds annually (n = 1).

a) continued Use ^ to indicate the power.

b) Calculate the return (A) if the bank compounds quarterly (n = 4).

c) Calculate the return (A) if the bank compounds monthly (n = 12).

d) Calculate the return (A) if the bank compounds daily (n = 365).

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

Answer 1

Formula should be A=P (1+r/n)^(nt). The 1+r/n is the growth factor each compounding period, and (nt) is the number of compounding periods.

a) for n = 1, A = 10,000(1+.1/1)^2 =12,100

b) for n = 4, 1+0.10/4 = 1.025, so A = 10,000(1.025)^8 = 12,184.02898

c) for n = 12, A = 10k(1 + 0.1/12)^24 = 12,203.90961

d) for n = 365, A = 10k(1 + 0.1/365)^730 = 12,213.69302

e) increase gets smaller -- diminishing returns, (1 + .1/n)^n → e as n → ∞.

Answer 2

a)12100
b)121.54.03
c)12203.91
d)122.13
e)12213.69
e) increases slowly but more when you decrease the compound period