Question

You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made in one month? What if the first payment is made today? You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay?

Answer 1

If your desired return is 3% per quarter then you will be willing to pay an amount of $50.

Step-by-step explanation:

To calculate how much you need to deposit on a monthly basis to have $1 million for retirement in 35 years with a monthly interest rate of 1%, you can use the present value of an annuity formula.

This complex financial calculation involves determining the required periodic payments to reach a future value given an interest rate over a set period of time.

For the payment made today, you would use the formula for the present value of an annuity due. In contrast, for the payment made in one month, you'd use the ordinary annuity formula. Since this was not solved in the explanation, the numeric solutions are not provided here.

Regarding the preferred stock paying quarterly dividends of $1.50, with a desired return of 3% per quarter, the price you would be willing to pay for the stock can be calculated using the dividend discount model (DDM).

This model considers the present value of future dividends at a required rate of return:

P = D / r

Where P is the price you should be willing to pay, D is the dividend paid, and r is the required rate of return.

Substituting our values:

P = $1.50 / 0.03

= $50

Therefore, you would be willing to pay $50 for the preferred stock.