Question

How long will it take a $1000 investment to triple in value at a .12% rate of return, compounded quarterly?

Answer 1

Answer:

n = 290

Step-by-step explanation:

Cq = P[(1 + r) ^ (4n) – 1]

• Cq is the quarterly compounded interest (Triple $1000 = $3000)
• P would be the principal amount ($1000)
• r is the quarterly compounded rate of interest (0.12%)
• n is the number of periods (Unknown)

Let's solve!

Cq = P[(1 + r) ^ (4n) – 1]

$3000 = $1000 * [(1 + 0.12%) ^ (4 * n) - 1]

3 = [(1 + 0.12%) ^ (4 * n) - 1]

3 = (1 + 0.12%) ^ (4 * n) - 1

4 = (1 + 0.12%) ^ (4 * n)

4 = (1 + 0.0012) ^ (4 * n)

4 = (1.0012) ^ (4 * n)

4 = (1.0012) ^ (4n)

Take a log to get rid of the n in the exponent

(1.0012) ^ (4n) = 4

log[(1.0012) ^ (4n)] = log(4)

4n * log(1.0012) = log(4)

4n = log(4) / log(1.0012)

4n = 0.60206 / 0.0005208

4n = 1156.02919

n ≈ 289.007297

Since the question asks how long it will take, you will round up, as it won't be fully tripled by 289, only by 290.