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18 July, 00:48

A person invests 5000 dollars in a bank. The bank pays 6.5% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 11300 dollars?

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Answers (2)
  1. 18 July, 01:17
    0
    Answer: 13.6 years

    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 = $5000

    A = $11300

    r = 6% = 6/100 = 0.06

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

    Therefore,.

    11300 = 5000 (1 + 0.06/12) ^12 * t

    11300/5000 = (1 + 0.005) ^12t

    2.26 = (1.005) ^12t

    Taking log of both sides, it becomes

    Log 2.26 = 12tlog 1.005

    0.354 = 12t * 0.0022

    0.354 = 0.0264t

    t = 0.354/0.026

    t = 13.6 years
  2. 18 July, 02:46
    0
    19.38 Months, so 1.6 years

    Step-by-step explanation:

    6.5% compounded monthly is $325 a month (5,300*.065) so if you subtract 11,300-5,000 you get $6,300. You divide that by 325 and you get 19.38 (months) divide that by 12 months and you get 1.6 (years)
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