To calculate the time it takes for 1,500 to grow to 1,782.87 at 8% monthly compounding, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the initial principal (1,500)
r = the annual interest rate (8%)
n = the number of times the interest is compounded per year (12 for monthly compounding)
t = the time in years
Substituting the given values, we get:
1,782.87 = 1,500(1 + 0.08/12)^(12t)
Dividing both sides by 1,500 and taking the natural logarithm of both sides, we get:
ln(1.18858) = 12t ln(1.00667)
Dividing both sides by 12 ln(1.00667), we get:
t = ln(1.18858)/(12 ln(1.00667)) = 2.92 years (rounded to two decimal places)
Therefore, it will take approximately 2.92 years, or 35 months, for 1,500 to grow to 1,782.87 at 8% monthly compounding.