Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,740?

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pagac.jessyca · Accepted Answer

Answer: 17 yearsStep-by-step explanation:The formula for the value of an account earning compound interest can be used to find the number of years. That formula is ... A = P(1 +r/n)^(nt)where P is the principal invested at annual rate r compounded n times per year for t years.__Solving for t, we find ... A/P = (1 +r/n)^(nt) . . . . . . divide by P log(A/P) = ntlog(1 +r/n) . . . . take logarithms t = log(A/P)/(nlog(1 +r/n)) . . . . . divide by the coefficient of tFor the given values, the time required is ... t = log(1740/670)/(365log(1 +0.055/365)) 17.353It would take about 17 years for the account value to reach $1740._____Additional commentThe time-value-of-money (TVM) apps of your calculator or spreadsheet can be used to find the time period of interest. Here, setting P/Y = 1 gives N in years.

Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,740?

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