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Chan deposited money into his retirement account that is compounded annually at an interest rate of 7 % . Chan thought the equivalent quarterly interest rate would be 2 % . ls Chan correct ? If he is , explain why . If he is not correct , state what the equivalent quarterly interest rate is and show how you got your answer.

Respuesta :

Answer:  No, He is not correct.

Step-by-step explanation:

Let the total amount deposited = P

Then the Amount in 1 year at the annually compound rate of 7%,

[tex]A_1 = P(1+\frac{7}{100} )[/tex]

[tex]A_1 = 1.07 P[/tex]

And, the amount in 1 year at the quarterly compound rate of 2%,

[tex]A_2 = P(1+\frac{2}{100})^4[/tex]  ( By the formula,  [tex]A = P(1+ \frac{r/n}{100} )^{4n}[/tex] )

[tex]A_2 =1.08243216 P[/tex]

But,  [tex]A_1<A_2[/tex]

Therefore, He is not correct.



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