Two certificates of deposit pay interest at rates that diffe

Two certificates of deposit pay interest at rates that differ by 3%. Money invested for one year in the first CD earns $120 interest. The same principal invested in the other CD earns $180. Find the two rates of interest.

Solution

A = P × (1 + r/n)nt

Where:
A = ending balance
P = initial deposit amount
r = annual nominal interest rate
t = number of years
n = number of compounding periods per year

Let the principal be P and rates of interest be x and y.

given y - x = 3

t = n = 1

A = P × (1 + r/n)nt implies

CD 1 : P+120= P(1 + x)

Px = 120

CD 2 : P+180= P(1 + x + 3)

180 = (3+x)120/x

3x = 6 + 2x

x=6(smaller value)

y = 9(larger value)