Question

Suppose $1,000 is deposited in a bank account today (time 0), followed by $1,000 deposits in years 2, 4, 6, and 8. At 6% annual interest, how much will the future equivalent be at the end of year 12?

Suppose that annual income from a rental property is expected to start at $1,300 per year and decrease at a uniform amount of $50 each year after the first year for the 15-year expected life of the property. The investment cost is $8,000, and i is 9% per year. Is this a good investment? Assume that the investment occurs at time zero (now) and that the annual income is first received at EOY one

It is likely that your college tuition will increase an average of 8% per year for the next 4 years. The annual cost of tuition at the beginning of your freshman year in college will be $12,000 (A1). How much money will you and your parents have to deposit in a mutual fund account one year prior to your freshman year to pay for your tuition for the 4 years you will spend earning your degree in engineering? The mutual fund will earn an average of 5% annual interest

Answer 1

The future value of deposits is found using the following equation

Future equivalent at end of year 12 = $ 8077.89

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To know if this is a good investment, we have to find the present value of the investment.

Present value of investment = - Initial cost + Present value of uniform payment - present value of deceasing gradient

Present value of investment = - $ 8000 + $ 10478.89 - $ 50 43.81

Present value of investment = $ 288.39 $ 288.4

This is a good investment because it produces a positive present value.

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The first step is to find the size of annual tution payments using future value of growing annuity equation.

Size of tution payments = $ 57,993.1

The amount to be deposited one year prior to the freshman year is found as follows

Amount to be deposited = $ 55231.5 $ 55232