*Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7% . Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander 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.*

Let the quarterly interest rate be a%

This means that each quarter his money would increase by a%.

Let P0 be his money at the beginning of the 1st quarter.

At the end of the 1st quarter, his money will increase to P1 = P0*(1 +a).

At the end of the 2nd quarter, his money will increase to P2 = P1*(1 +a) = P0*(1+a)^2.

At the end of the 3rd quarter, his money will increase to P3 = P2*(1 +a) = P0*(1+a)^3.

At the end of the 4th quarter, his money will increase to P4 = P3*(1 +a) = P0*(1+a)^4.

We are told that his money will be increased by 7% over one year. i.e. it will be P0*(1 + 7%)

So, if 2% is the equivalent quarterly rate, then P0*(1 + 0.07) = P0*(1 + 0.02)^4

i.e. 1.07 = 1.02^4

but 1.02^4 = 1.0824

**So Alexander is wrong. 2% is too large to be an equivalent quarterly rate.**

The true quarterly rate is given by solving the equation,

1.7 = (1 + a/100)^4

(1 + a/100)^2 = √(1.07) = 1.0344

1 + a/100= √(1.0344) = 1.01706

**a = 1.7%**

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