Answer:
n = 290
Step-by-step explanation:
Cq = P[(1 + r) ^ (4n) – 1]
- Cq is the quarterly compounded interest (Triple $1000 = <u>$3000</u>)
- P would be the principal amount <u>($1000)</u>
- r is the quarterly compounded rate of interest <u>(0.12%)</u>
- n is the number of periods <u>(Unknown)</u>
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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.
