Time Value of Money

You deposit $$1,000$ in a bank account. The bank pays you $8\%$ interest compounded quarterly. $18$ months later, you decide to close the account. What will be the amount in your account after $18$ months?

If you need $$20,000$ after three years and you can invest your funds in account that earns $10\%$ per year, compounded semiannually, how much must you deposit in the account today?

You start saving for yourcollege education. You begin college at the age of $18$ and you will need $$10,000$ per year at the beginning of each year of college. You will make a deposit one year from today in an account that pays $6\%$ compounded annually and an identical deposit each year, with the last deposit on your ${17}^{th}$ birthday. If an annual deposit of $$8,396$ will allow you to reach your goal, how old are you now?

You are now $20$ years old. You want to buy Nissan $200Zx$ when you are $27$ years old. The current price of the car is $$25,000$ and you expect a $10\%$ increase in this price per year. If you are earning $14\%$ from your investments, what should your annual savings be$?($savings will be in equal amounts$)$

You decided to buy microwave equipments for your new factory. The cost of the equipments is $$8,795.$ The seller offers you a payment plan. According to this plan at the beginning you will make a down payment of $$2,000.$ And you will pay the rest of your debt in equal payments in $4$ years, at an interest rate of $12\%,$ compounded quarterly. What will your annual payments be$?$