What is the future value three years hence of $1,000 invested in an account with

Question

What is the future value three years hence of $1,000 invested in an account with a stated annual interest rate of 8 percent, compounded annually? compounded semiannually? compounded monthly? compounded continuously? Why does the future value increase as the compounding period shortens? Calculate the present value of $5,000 received 12 years from today. Assume a stated annual interest rate of 10 percent, compounded quarterly. Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly, while Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly. In which bank should you deposit your money?

Explanation / Answer

Ans. 3.11 Future Value= PV*(FV factor for n,i)= PV*(1+i)n

If we know the single amount (PV), the interest rate (i), and the number of periods of compounding (n), we can calculate the future value (FV) of the single amount. Calculationsto determine the future value (FV) through the use of future value factors are as below.

a)Here PV= $1000,i=8% ,n= 1 for 3 yrs

FV= $1000*(1.08)3= $1259.71

b)Here PV= $1000,i=8% ,n= 2 for 3 yrs

FV= $1000*(1+(0.08/2))2*3= $1000*(1.04)6 =$1265.32   

c)Here PV= $1000,i=8% ,n= 12 for 3 yrs

FV= $1000*(1+(0.08/12))12*3

=1000*(1.00667)36 =$1270.24

d)Here PV= $1000,i=8% ,n= assume 100 as it is continously as period is not specified clearly

FV= $1000*(2199.76126).= $21,99,761.26

e)The future value increases because of the compounding. The account is earning

interest on interest. Essentially, the interest

is added to the account balance at the end of

every compounding period. During the next period, the account earns interest on the new

balance. When the compounding period shortens, the balance that earns interest is risin faster.

Ans 3.12 present value of $5000

PV= FV/ (1+i)n

= $5000/(1+0.10)48

= $51.54

Ans 3.13 Assume Rs. 100 to be invested in Bank. in that case future value in both banks should be calculated as follows

Bank of America=FV= $100*(1.041)4 =$117.44

Bank of USA=FV= $100*(1.0405)12 =$161.03

So one should invest in Bank of USA because shorten the period of compunding higher the return.

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