A formula that could be used to find the future value of Timothy's account after n months is: [tex]A = 1005^{\frac{144}{n} }[/tex]
Given the following data:
- Number of times compounded = 12
- Time = n months to years = [tex]\frac{12}{n} \;years[/tex]
To write a formula for the Amount A Timothy has after n months:
Mathematically, compound interest is given by the formula:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where;
- P is the principal or starting amount.
- r is annual interest rate.
- n is the number of times the interest is compounded in a year.
- t is the number of years for the compound interest.
Substituting the given parameters into the formula, we have:
[tex]A = 1000(1 + \frac{0.06}{12} )^{12\times \frac{12}{n} }\\\\A = 1000(1 + 0.005 )^{\frac{144}{n} }\\\\A = 1000(1.005 )^{\frac{144}{n} }\\\\A = 1005^{\frac{144}{n} }[/tex]
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