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Tyron is saving up money for a down payment on a motorcycle. He currently has $5648, but knows he can get a loan at a lower interest rate if he can put down $6355. If he invests the $5648 in an account that earns 6% annual, compounded monthly, how long will it take Tyron to accumulate the $6355

Respuesta :

Answer:

monthly  time  = 1.966

Explanation:

given data

final amount = $6355

initial principal = $5648

rate = 6 %

solution

we get here time by this formula

amount = principal × [tex](1+r)^{t}[/tex]    ............1

put here value and we get time t

6355 = 5648 × [tex](1+\frac{0.06}{12})^{12\times t}[/tex]    

1.125 = [tex](1.005)^{12\times t}[/tex]  

take ln both side

ln 1.125 = ln  [tex](1.005)^{12\times t}[/tex]  

0.1177 = 12 × t × 4.9875 × [tex]10^{-3}[/tex]  

monthly  time  = 1.966

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