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**

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