Question

Please Help,

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.

Answer 1

Answer: No, He is not correct.

Explanation:

Let the total amount deposited = P

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

`A_1 = P(1+(7)/(100) )`

`A_1 = 1.07 P`

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

`A_2 = P(1+(2)/(100))^4` ( By the formula,
`A = P(1+ (r/n)/(100) )^(4n)` )

`A_2 =1.08243216 P`

But,
`A_1<A_2`

Therefore, He is not correct.