Question

The equation below shows that the value of a $4,800 certificate of deposit (CD)
n
years in the future will be $5,000.



5
,
000
=
4
,
800
(
1
+
0
.
03
)
n



What is the approximate amount of time that must pass before the CD will have a value of $5,000?


1.4 years


1.8 years


2.6 years


3.7 years

Answer 1

Solve for n: 5000 = 4800(1.03)^n → (1.03)^n = 5000/4800 = 1.041666...

Take logs: n = ln(1.0416667)/ln(1.03) ≈ 0.04082/0.02956 ≈ 1.38 ≈ 1.4 years.

Answer: 1.4 years.