how long will it take to increase a $2,200 investment to $10,000 if the interest rate is 6.5 percent? - brainly.com (2024)

To calculate how long it will take for a $2,200 investment to increase to $10,000 at an interest rate of 6.5 percent, we need to use the formula for compound interest.The formula for compound interest is:A = P(1 + r/n)^(nt)Where:A is the final amountP is the principal amount (initial investment)r is the annual interest rate (expressed as a decimal)n is the number of times interest is compounded per yeart is the number of yearsIn this case, the principal amount (P) is $2,200, the final amount (A) is $10,000, and the annual interest rate (r) is 6.5 percent, which is equivalent to 0.065 as a decimal.Let's assume that interest is compounded annually, so n is equal to 1.Now, let's plug in the given values into the formula and solve for t:$10,000 = $2,200(1 + 0.065/1)^(1*t)Simplifying the equation, we get:4.5455 = (1.065)^tTo solve for t, we can take the logarithm of both sides of the equation:log(4.5455) = log((1.065)^t)Using logarithm properties, we can bring down the exponent:log(4.5455) = t*log(1.065)Now, we can isolate t by dividing both sides of the equation by log(1.065):t = log(4.5455)/log(1.065)Using a calculator, we can find that t is approximately 15.29 years.Therefore, it will take approximately 15.29 years for a $2,200 investment to increase to $10,000 at an interest rate of 6.5 percent compounded annually.