Finance

Money has time value associated with it. This time value principle implies that a dollar received today worth more than a dollar to be received tomorrow (or in future).

The future and the present value of money are based on the time (number of periods) involved and the implicit interest rate.

Problem a
You are saving for retirement. To live comfortably, you decide you will need to save 2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into savings account. If the interest rate is 5, how much must you set aside each year to make sure that you will have 2 million in the account on your 65th birthday

Conclusion
An amount of   22,143.49 should be set aside every year, starting from 30th birthday, in an account yielding 5 annually, until 65th birthday to have  2,000,000 in the account on 65th birthday.

Problem b
Because your income will increase over your lifetime, it would be more realistic to save less now and more later. Instead of putting the same amount aside each year, you decide to let the amount that you set aside grow by 7 per year. Under this plan, how much will you put into the account today to have 3641 in 3 years (Recall that you are planning to make the first contribution to the account today.)

Solution
EMBED Excel.Sheet.8

Conclusion
An amount of   2,972.14 should be put in to the account today yielding 7 annually, to have  3,641 in the account in 3 years time.

Future recommendations
Money always has a time-associated value. This is because of the opportunity to receive money in future is not as valuable as cash received today. This concept allows comparison of cash flows available at different point of time. However, the cash flows received at different points of time are not additive, and require certain adjustments for risks associated with such cash flows.