CP

Solving for n

Suppose you invest $78.35 at an interest rate of 5 percent per year. How long will it

take your investment to grow to $100? You know PV, FV, and i, but you do not know

n, the number of periods. Here is the situation:

Time Line:

05%1 2 n
1n?

...

78.35 100

Equation:

(2-1)

1. NUMERICAL SOLUTION

Use Equation 2-1 to solve for n:

$100 $78.35 (1 0.05)n.

Transform to:

$100/$78.35 1.276 (1 0.05)n.

Take the natural log of both sides, and then solve for n:

n LN(1.05) LN(1.276)

n LN(1.276)/LN(1.05)

Find the logs with a calculator, and complete the solution:

n 0.2437/0.0488

4.9955 
5.0.

Therefore, 5 is the number of years it takes for $78.35 to grow to $100 if the interest

rate is 5 percent.

2. FINANCIAL CALCULATOR SOLUTION

Inputs: 5 
78.35 0 100

Output: 5.0

Enter I 5, PV 
78.35, PMT 0, and FV 100, and then press N to get

N 5.

$100$78.35(1.05)n. Solve for n.

FVnPV(1i)n

Solving for Interest Rate and Time 69

Time Value of Money 67