Question

1a.)Calculate, to the nearest cent, the present value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. HINT [See Quick Example 4.]

5 years, at 5.2% per year, compounded weekly (52 times per year)

1b.) Find the effective annual interest rate r of the given nominal annual interest rate. Round your answer to the nearest 0.01%.

13% compounded monthly

1c.) Compute the specified quantity.

You take out a 5 month, $4,000 loan at 8% annual simple interest. How much would you owe at the end of the 5 months (in dollars)? (Round your answer to the nearest cent.)

Answer 1

a.We use the formula:  
A=P(1+r/52)^52n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

1000=P*(1+0.052/52)^(52*5)

P=1000/(1+0.052/52)^(52*5)

=1000*0.771151762

=$771.15(Approx)

b.EAR=[(1+APR/m)^m]-1
where m=compounding periods

=[(1+0.13/12)^12]-1

=13.80%(Approx)

c.Simple interest=Principal*Interest rate*Time period

=4000*8%*(5/12)

=133.33

Future value=Principal+Simple interest

=4000+133.33

=$4133.33(Approx)