Question

Find the following values. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent. a. An initial $700 compounded for 10 years at 10%. $ b. An initial $700 compounded for 10 years at 20%. $ c. The present value of $700 due in 10 years at 10%. $ d. The present value of $2,355 due in 10 years at 20% and 10%. Present value at 20%: $ Present value at 10%: $ e. Define present value. The present value is the value today of a sum of money to be received in the future and in general is less than the future value. The present value is the value today of a sum of money to be received in the future and in general is greater than the future value. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value. The present value is the value in the future of a sum of money to be received today and in general is less than the future value. The present value is the value in the future of a sum of money to be received today and in general is greater than the future value.

Answer 1

a.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=700*(1.1)^10

=700*2.59374246

=$1815.62(Approx)

b.We use the formula:  
A=P(1+r/100)^n
where   
A=future value
P=present value  
r=rate of interest
n=time period.

A=700*(1.2)^10

=700*6.19173642

=$4334.22(Approx)

c.Present value=700*Present value of discounting factor(rate%,time period)

=700/1.1^10

=700*0.385543289

=$269.88(Approx)

d.At 20%:Present value=2,355*Present value of discounting factor(rate%,time period)

=2,355/1.2^10

=2,355*0.161505583

=$380.35(Approx)

At 10%:Present value=2,355*Present value of discounting factor(rate%,time period)

=2,355/1.1^10

=2,355*0.385543289

=$907.95(Approx)

e.Present value is the value today of a future cash flow/future group of cash flows at a specified interest rate for a specified period of time.Hence present value is lesser than future cash flow

Hence the correct option is:

The present value is the value today of a sum of money to be received in the future and in general is less than the future value.