Question

Find the present value of $700 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

A) 10% nominal rate, semiannual compounding, discounted back 5 years

B) 10% nominal rate, quarterly compounding, discounted back 5 years

C) 10% nominal rate, monthly compounding, discounted back 1 year  

Answer 1

Answer to Requirement A.

Future Value = $700
Present Value = ??
Rate = 10% p.a. or 5.00% semi-annually
Time = 5 years or 10 semi-annual period

Future Value = Present Value * (1+ r)^n
$700 = Present Value * (1 + 0.05)^10
$700 = Present Value * 1.05^10
$700 = Present Value * 1.6289
Present Value = $429.74

Answer to Requirement B.

Future Value = $700
Present Value = ??
Rate = 10% p.a. or 2.50% quarterly
Time = 5 years or 20 Quarters

Future Value = Present Value * (1+ r)^n
$700 = Present Value * (1 + 0.025)^20
$700 = Present Value * 1.025^20
$700 = Present Value * 1.6386
Present Value = $427.19

Answer to Requirement C.

Future Value = $700
Present Value = ??
Rate = 10% p.a. or 0.83% monthly
Time = 1 years or 12 months

Future Value = Present Value * (1+ r)^n
$700 = Present Value * (1 + 0.00833)^12
$700 = Present Value * 1.00833^12
$700 = Present Value * 1.1047
Present Value = $633.66