A person invests 6000 dollars in a bank. The bank pays 6.25% interest compounded monthly. The person leaves the money in the bank until it reaches 8800 dollars for 6.1 years.
How does compounding work?
Suppose that the initial amount of something is P.
Let after one unit of time, it increases by R% (per unit time) and compounds on the resultant total of that quantity, then, after T such units of time, then the quantity would increase to:
[tex]A = P(1 + \dfrac{R}{100})^T[/tex]
A person invests 6000 dollars in a bank. The bank pays 6.25% interest compounded monthly.
Given that :
Principal = 6000
Interest (r) = 6.25% compounded annually
Calculate time, t, if final amount A = 8800
Using the compound interest formula
[tex]A = P(1 + \dfrac{R}{100})^T[/tex]
A = final amount
n = number of times interest is applied per period
[tex]8800 = 6000(1 + {0.0625})^{t}[/tex]
[tex]8800 = 6000(1 + {0.0625})^{t}\\\\\\8800 = 6000({1.0625})^{t}\\\\\\\dfrac{8800} {6000}=({1.0625})^{t}\\\\\\1.46 =({1.0625})^{t}[/tex]
Take the log of both sides
[tex]log 1.46 = t log 1.0675\\\\0.1643 = 0.0263289t\\\\t = 6.1[/tex]
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