We use the formula:
A = P(1+r/n)nt
A = total amount
P = principle investment
r = interest rate
n = # of time intervals in a year
t = # of years
(the letters used to represent these may differ for your class, but use of the formula is the same,)
Part a:
P = 100
r = 12% = .12
t = 1
A is unknown
For annual interest, n=1 (there is 1 year in a year) so we can solve:
A = 100(1+.12/1)1*1= $112
Semiannually n=2 (2 semi years in a year.)
A = 100(1+.12/2)2*1= $112.36
Monthly n=12 (12 months in a year)
A = 100(1+.12/12)12*1 = 112.682503 ≈ $112.68
b. The same formula, but slightly different given values.
A = 100
t = 1
r = 12% = .12
P is unknown.
Annually
100 = P(1+.12/1)1*1
100 = P(1.12)
P = 89.28571429 ≈ $89.29
Semiannually
100 = P(1+.12/2)2*1
100 = P(1.06)2
100 = P(1.1236)
P = 88.999644 ≈ $89.00
Monthly
100 = P(1+.12/12)12*1
100 = P(1.01)12
100 = P(1.12682503)
P = 88.74492253 ≈ $88.74