Question

three years ago, pablo invested $1000. in 2 years, he expects to have $2830. if pablo expects to earn the same annual rate of return after 2 years from today as the annual rate implied from the past and expected values given in the problem, then how much does he expect to have in 5 years from today?(round the value to 100th decimal)

Answer 1

Answer: Pablo expects to have $8000.58 in 5 years from today.

Explanation: To solve this problem, we can use the formula for compound interest, which is:A = P(1 + r/n)^(nt)Where: A = the final amount, P = the principal or initial investment, r = the annual interest rate, n = the number of times the interest is compounded per year, t = the time period in years.

First, we need to find the annual interest rate implied by the given information. To do this, we can use the formula for the annual percentage rate (APR):APR = 100[(1 + r/n)^n - 1] where n = the number of times the interest is compounded per year. For the first two years, Pablo's investment grew from $1000 to $2830. Therefore, the interest earned during this time was $2830 - $1000 = $1830. Using the formula for compound interest, we can solve for the annual interest rate: r = n[(A/P)^(1/nt) - 1]Plugging in the values we have:r = 1[(2830/1000)^(1/(2*1)) - 1]r = 0.4142 or 41.42%Using this annual interest rate, we can find how much Pablo expects to have in 5 years: Let P = $2830 (the amount he expects to have after 2 years) A = P(1 + r/n)^(nt)A = 2830(1 + 0.4142/1)^(1*5)A = 2830(1.4142)^5A = 2830(2.8284)A = 8000.58