Question

Find the following values using the equations and then a financial calculator. Compounding/discounting occurs annually. Do not round intermediate calculations. Round your answers to the nearest cent.

1. An initial $200 compounded for 1 year at 7%.

   $  

2. An initial $200 compounded for 2 years at 7%.

   $  

3. The present value of $200 due in 1 year at a discount rate of 7%.

   $  

4. The present value of $200 due in 2 years at a discount rate of 7%.

   $  

Answer 1

a. Initial amount = Present value = $200, Time = 1 year, Interest rate = 7%,, To find future value or FV after 1 year of compounding

We know that Future value = Present value (1+interest rate)^{Time period}

Future value = 200(1+7%) = 200 x 1.07 = 214

We can find the Future value by using financial calculator. In financial calculator we enter

PV = -200, PMT = 0, I/Y = 7%,NPER = 1 then find or compute FV

we get FV = 214

Note: PMT = 0 because there are no annual payments

Answer $214

b.

Initial amount = Present value = $200, Time = 2 year, Interest rate = 7%,, To find future value or FV after 2 year of compounding

We know that Future value = Present value (1+interest rate)^{Time period}

Future value = 200(1+7%)² = 200 x (1.07)² = 200 x 1.1449 = $228.98

We can find the Future value by using financial calculator. In financial calculator we enter

PV = -200, PMT = 0, I/Y = 7%,NPER = 2 then find or compute FV

we get FV = 228.98

Note PMT = 0 because there are no annual payments

Answer: $228.98

c. Amount due in 1 year = Future value = $200, Time period = 1 year, interest rate = discount rate = 7%, To find present value or PV

We know that

Present value = Future value / (1+interest rate)^{Time period} = 200 / (1+7%)¹ = 200 / 1.07 = 186.9158 = 186.92 (rounded to nearest cent)

We can find the Future value by using financial calculator. In financial calculator we enter

FV = -200, PMT = 0, I/Y = 7%,NPER = 1 then find or compute PV

we get PV = 186.9158

Note PMT = 0 because there are no annual payments

PV = 186.9158 = 186.92 (rounded to nearest cent)

Answer: $186.92

d. Amount due in 2 year = Future value = $200, Time period = 2 year, interest rate = 7%, To find present value or PV

We know that

Present value = Future value / (1+interest rate)^{Time period} = 200 / (1+7%)² = 200 / 1.1449 = 174.6877 = 174.69 (rounded to nearest cent)

We can find the Future value by using financial calculator. In financial calculator we enter

FV = -200, PMT = 0, I/Y = 7%,NPER = 2 then find or compute PV

we get PV = 174.6877

Note PMT = 0 because there are no annual payments

PV = 174.6877 = 174.69 (rounded to nearest cent)

Answer: $174.69