Ask Question
7 August, 06:56

In 1624 , an explorer convinced a group of indigenous peoples to sell him an island for $ 23. If the indigenous peoples had put the $ 23 into a bank account paying 8 % , how much would the investment be worth in the year 2002 if the interest were compounded a. quarterly ? b. continuously?

+1
Answers (1)
  1. 7 August, 07:53
    0
    a. $231,839,557,939,952.9

    b. $312,458,949,828,962

    Explanation:

    Total number of years of investment = final year - initial year

    = 2002 - 1624 = 378 years;

    Yearly rate of interest = 8%

    Total investment made in 1624 is = $23

    a) Interest when compounded quarterly

    A = P (1 + r/t) ^tn where A = final amount; P = Principal amount' r = rate of interest per year; t = number of terms of compounding in a year; n = number of years

    for quarterly compounding, t = 4 (as 4 times it gets compounded every year)

    n = 378 years

    P = $23

    r = 8% or r = 0.08

    Applying the formula we get:

    A = 23 (1 + 0.08/4) ^4*378

    A = 23 * 10079980779997.95

    A = $231,839,557,939,952.9

    Therefore, with a quarterly compounding, this investment would come out to be $231,839,557,939,952.9

    a) Interest when compounded quarterly

    In continuous compounding

    A = P * e^rt

    P = $23

    r = 8% or 0.08

    t = 378 years

    Substituting the values in the formula we get:

    A = 23 (e) 0.08*378

    A = 23 (e) 30.24

    A = 23 (13,585,171,731,694)

    A = $312,458,949,828,962

    Therefore, with a continuous compounding in place, 23$ investment, would amount to $312,458,949,828,962 by 2002.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “In 1624 , an explorer convinced a group of indigenous peoples to sell him an island for $ 23. If the indigenous peoples had put the $ 23 ...” in 📘 Business if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers