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To save for​ retirement, Karla Harby put ​$475 each month into an ordinary annuity for 19 years. Interest was compounded monthly. At the end of the 19 ​years, the annuity was worth ​$234 comma 341. What annual interest rate did she​ receive?

Respuesta :

Answer:

Annual interest will be 33.036 %

Explanation:

We have given initial amount P = $475

Time t = 19 years

As interest is compounded monthly

So number of period = 19×12 = 228 period

Final amount is given A = $234341

Amount is given by

[tex]A=P(1+\frac{r}{100})^n[/tex]

[tex]234341=475(1+\frac{r}{100})^{228}[/tex]

[tex]493.3494=(1+0.01r)^{228}[/tex]

[tex](1+0.01r)=(493.3494)^{\frac{1}{228}}[/tex]

[tex](1+0.01r)=1.027[/tex]

[tex]0.01r=0.027[/tex]

[tex]r=2.753[/tex] %

Annual interest = 12×2.753 =33.036 %

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