Answer:
5.09 years
Step-by-step explanation:
The formula for the future value of an investment can be filled with the given values and solved for time.
Formula
The future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
Application
Using this formula with the given values, we have an expression for t:
7300 = 5000(1 +0.075/4)^(4t)
Dividing by 5000, we have ...
1.46 = 1.01875^(4t)
Taking logarithms gives the linear equation ...
log(1.46) = 4t·log(1.01875)
Dividing by the coefficient of t, we find ...
t = log(1.46)/(4·log(1.01875)) ≈ 5.0929
The time required for the value to reach $7300 is about 5.09 years.
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Additional comment
The attachments show different calculator solutions. They give the same value for t.
The TVM Solver uses P/Y = 1 so the value of N is in years.
The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.
