You will therefore have interest, at least $[tex]2000[/tex] in the account after approximately 8 years and 5 months.
When calculating interest over time, use the following formula:
A = P [1 + (r/n)] ^(nt) .where n = how many times you compound during a year, t = time in years, A = new amount in the account, P = principal, r = percent rate as a decimal, and
[tex]A = 2000 \sP = 1500 \sr = 0.035 \sn=1[/tex]
So, you obtain:
[tex]2000 = 1500 (1+0.035)^t[/tex]
Multiply by 1500:
[tex](4/3) = (1.035)^t[/tex]
Put "ln" to use on both sides:
[tex]ln(4/3) = t*ln (1.035)[/tex]
Do the logarithm calculations:
[tex]0.28768 = t*0.03440[/tex]
Divide both sides by[tex]0.03440:[/tex]
[tex]8.36[/tex] years, or t
You will therefore have at least $[tex]2000[/tex] in the account after approximately 8 years and 5 months.
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