Keith needs 4698 for a future project. He can invest 3000 now at an annual rate of 10.2%, compounded monthly. Assuming that no withdrawals are made, how long will it take for him to have enough money for his project? Do not round any intermediate computations, and round your answer to the nearest hundredth.

To find out how long it will take for Keith to have enough money for his project, we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where: A = the future value of the investment P = the principal amount (initial investment) r = annual interest rate (as a decimal) n = number of times interest is compounded per year t = number of yearsIn this case, Keith's initial investment is $3000, the annual interest rate is 10.2% (or 0.102 as a decimal), and interest is compounded monthly (so n = 12).We need to solve for t, so we rearrange the formula:A/P = (1 + r/n)^(nt)Substituting the given values:4698/3000 = (1 + 0.102/12)^(12t)Dividing both sides by 3000:1.566 = (1 + 0.0085)^(12t)Taking the natural logarithm of both sides:ln(1.566) = ln((1 + 0.0085)^(12t))Using the property of logarithms that ln(a^b) = b * ln(a):ln(1.566) = 12t * ln(1 + 0.0085)Dividing both sides by 12 * ln(1 + 0.0085):t = ln(1.566) / (12 * ln(1 + 0.0085))Using a calculator, we find:t ≈ 4.91Therefore, it will take approximately 4.91 years for Keith to have enough money for his project.