Final answer:
It will take approximately 5 years for $1,000 to increase to $3,000 with 3.2% compound quarterly interest.
Step-by-step explanation:
To find out how long it will take for $1,000 to increase to $3,000 with 3.2% compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount ($3,000 in this case)
- P is the principal amount ($1,000 in this case)
- r is the annual interest rate (3.2%, or 0.032, in this case)
- n is the number of times interest is compounded per year (quarterly, so n = 4 in this case)
- t is the number of years
Plugging in the values, we get:
$3,000 = $1,000(1 + 0.032/4)^(4t)
Simplifying, we have:
3 = (1.008)^(4t)
To solve for t, we need to take the logarithm of both sides:
log(3) = log((1.008)^(4t))
Using logarithmic properties, we can bring down the exponent:
log(3) = 4t * log(1.008)
Dividing both sides by 4log(1.008) gives:
t = log(3) / (4 * log(1.008))
Calculating this value gives t ≈ 5.13 years. Rounding to the nearest year, it will take approximately 5 years for $1,000 to increase to $3,000 with 3.2% compound quarterly interest.