Ask Question
26 February, 18:36

Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $49,300?

+5
Answers (1)
  1. 26 February, 19:03
    0
    Answer: it will take 7 years for the value of the account to reach $49,300

    Step-by-step explanation:

    We would apply the formula for determining compound interest which is expressed as

    A = P (1 + r/n) ^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = $41000

    A = $49300

    r = 2.6% = 2.6/100 = 0.026

    n = 12 because it was compounded 12 times in a year.

    Therefore,

    49300 = 41000 (1 + 0.026/12) ^12 * t

    49300/41000 = (1 + 0.0022) ^12t

    1.2024 = (1.0022) ^12t

    Taking log of both sides of the equation, it becomes

    Log 1.2024 = 12t * log 1.0022

    0.08 = 12 * 0.00095 = 0.0114t

    t = 0.08/0.0114

    t = 7 years
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Emma invested $41,000 in an account paying an interest rate of 2.6% compounded monthly. Assuming no deposits or withdrawals are made, how ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers