Answer:
Time ≈ 3.25 years
Explanation:
Formula for compound interst:
The formula for compound interest is given by:
A(t) = P(1 + r/n)^(nt), where
- A(t) is the amount in the account after t years,
- r is the interest rate (the percentage is converted to a decimal when using the formula),
- and n is the number of compounding periods.
Determining n (the number of compounding periods):
- Note that when money is compounded quarterly, there are 4 compounding periods.
- This means the money is compounded once every 3 months and there are four of these 3-month periods in 1 year (i.e., 12 months).
Using the compound interest formula:
Now we can solve for t (the amount of time in years) by substituting 6145 for A, 5000 for P, 0.064 for r, and 4 for n:
(6145 = 5000(1 + 0.064/4)^(4t)) / 5000
log (1.229) = log ((1.016)^4t)
(log (1.229) = 4t * log(1.016)) / log (1.016)
(log (1.229) / log (1.016) = 4t) * 1/4
1/4 * (log (1.229) / log (1.016)) = t
3.247594892 = t
3.25 = t
Thus, it would take about 3.25 years for the $5000 investment to grow to $6145, given that there's a 6.4% annual interest rate and that the money is compounded quarterly.