• anonymous
Ramona deposited $4,190.51 into a savings account with an interest rate of 5.2% compounded twice a year. About how long will it take for the account to be worth $9,000?
  • Stacey Warren - Expert
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  • katieb
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  • jdoe0001
  • jdoe0001
so as you can see from the above formula, what is required is to "solve" or to find "t" so the A or "balance" will be 9000 4,190.51 is the principal, or starting amount from the rate is 5.2% or 5.2/100 = 0.052 the "n" period per year is 2, since it's being compounded twice a year so now $$ 9000 = 4190.51\pmatrix{1+\cfrac{0.052}{2}}^{2t}\\ \cfrac{9000}{4190.51}=\pmatrix{1+\cfrac{0.052}{2}}^{2t}\\ 2.15 = 1.026^{2t}\\ -----------------\\ \text{use log cancellation rule}\\ \color{blue}{log_{1.026}} (2.15) = \color{blue}{log_{1.026}}(1.026^{2t})\\ \color{blue}{log_{1.026}}(2.15) = 2t\\ -----------------\\ \text{using log change of base rule}\\ \cfrac{log_{10} (2.15)}{log_{10}(1.026)} = 2t $$ now all you need to do is solve for "t" :)

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