Question

Future Value of Account A Note: Account A pays simple interest. Future Value Principal + Interest Principal + [(Principal x Interest Rate) x Investment Period] $2,000 + [($2,000 x 6%) x 3 years] Future Value of Account X Note: Account X pays compound interest. Future Valuex = Present Value x Interest Rate Factor Present Value x (1 + Interest Rate)N $2,000 (1 + 0.06)3 $ To find the interest rate factor, you can use four different ways, including multiplying it out: Interest Factor = (1 + 0.06) (1 + 0.06) x (1 + 0.06) 1.1910 Or you can use exponents, and calculate it directly: Interest Factor = (1 + 0.063 1.1910 The third alternative for solving the equations is to use a spreadsheet, and the fourth is to let a financial calculator perform the calculation. This requires that you know how your calculator functions and how to enter the following variables: 1 3 6% 2000 Input Keystroke Output P/Y N I PV FV Answer P/Y indicates the number of compounding periods per year, N is the number of years, I is the interest rate, PV is present value, and FV is future value. Difference in Future Values Difference FVX - FVA $

Answer 1

Recognition to the Time Value of money in financial decision making is extremely important. A financial decision taken today has implications for a no. of years, spread into the future. Time value of money means that the value of a unit of money is different in different time periods. The value of a sum of money received today is more than than its value received after some time. This time preference for money is because the money so received today will earn a rate of return if reinvested, which would not be possible if the same money is received at a later date.

The money that is received today is called the Principal. This Principal is called the Present Value of the cash flow. When that principal is reinvested to let it grow in the future at a particular rate of return which is called the interest rate.The money that grows over a certain periond of time (also called the Investment period) is called the Amount received in the future or the Furure Value of the Principal.
Interest rate in case of loans can also be defined as the amount charged on top of the principal by a lender to a borrower for the use of assets. Interest rates are of two types :- Simple & Compound.
Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. It can be expressed mathematically as:-

$I = P\times r\times T$

where, I = Simple Interest; P= principal;   T = Investment period in years

This type of interest usually applies to automobile loans or short-term loans.

Compound interest (or compounding interest) is interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. Interest can be compounded on any given frequency schedule, from daily to monthly, qaurtely, semi- annually or annually. When calculating compound interest, the number of compounding periods makes a significant difference.The rate at which compound interest accrues depends on the frequency of compounding or the compounding periods, such that the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period as the interest-on-interest effect can generate increasingly positive returns based on the initial principal amount.
The formula by which the future value of an amount is obtained by compounding technique can be expressed mathematically as follows:-

$A=P(1+i)^{n}$

wher, A = Future value of the principal amt.; P = principal; i = Interest rate, n = no. of years or the investment period.

Future Value of Account A in case of Account A pays Simple Interest :-

where, P = $2000, i = 6%, T or n i.e. the investment period = 3years

Therefore, Future ValueA = Principal + Interest

= $P+(P\times r\times T)$ = $2000 + ($2000 * 6% * 3) = $2000 + ($2000 * 0.06 * 3)

= $2000 + $360 = $2360

Hence, Future ValueA = $2360

Future Value of Account X in case of Account X pays Compound Interest :-  

Future ValueX = Present Value (1+ Interest rate)N {Present Value = Principal amt.}

= =
$2000 + (1.06)

= $2000 * 1.1910 { Since the interest factor (1.06)3 = 1.1910}

= $2382

Hence, Future ValueX = $2382

Difference in Future Values :-

FVX - FVA = $ (2382 - 2360) = $22

Dakota : Uh... If the interest rate were zero, then interest would (not be) earned by (Either Account); the future value of account A would be ($2,000); the future value of account X would be ($2,000); and the difference between the two accounts would be ($0).

Explanation :- If the interest rate is zero, money deposited today will be worth the exact same amount in the future also i.e. in above case after 3 years.