Question

How long will it take $10,000 to reach $50,000 if it earns 10% annual interest compounded semiannually?

Answer: 16.5 years

Please show steps to solving this, using the below Equation. I don't know what to put in for "e"

Equation 8-7. Future Value with Continuous Compounding:

?? = ?? ∗ ? ? ∗?

Where: FV = Future Value
PV = Present Value
e = Natural antilog of 1
n = Number of years
k = Stated annual interest rate (expressed as decimal)

Answer 1

Present Value (PV) = $10,000

Future Value (FV) = $50,000

Interest Rate (r) = 10%

Number of years (n) = ?

Formula to calculate FV = PV * (1 + r)ⁿ

As the interest is being compounded semiannualy, time period is doubled and the interest rate is halved.

Formula to calculate FV = PV * {1 + (r/2)}²ⁿ

Putting values given in the question,

$50,000 = $10,000 * {1 + (0.1/2)}²ⁿ

Therefore, 5 = (1.05)²ⁿ

Taking log both sides,

log (1.05)²ⁿ = log 5

2n * log (1.05) = log 5

After looking the values for log (1.05) and log 5 from the log table

2n * (0.0211) = (0.6989)

2n = 32.98

n = 16.49

n = ~16.5 years