Question

Calculate the future value in six years of $4,000 received today if your investments pay (Do not round intermediate calculations, and round answers to 2 decimal places please)

A). 6 percent compounded annually

B). 8 percent compounded annually

C). 10 percent compounded annually

D). 10 percent compounded semiannually

E). 10 percent compounded quarterly

Answer 1

Given,

Present value = $4000

Time period in years = 6

Future value = ?

A) 6% compounded annually

We know that the Future value formula is given by,

FV = PV*(1+(r/m))^mT

where,

FV = Future Value

PV = Present Value = 4000

r = annual interest rate = 6% = 0.06

T = number of years = 6

m = Number of periods based on compounding frequency = 1

Substituting these in the above formula, we get

FV = 4000*(1+(0.06/1))^(1*6)

FV = 4000*(1.06)^(6)

FV = 4000*1.4185

FV = 5674.08

Therefore, FV = $5674.08

B)8% compounded annually

We know that the Future value formula is given by,

FV = PV*(1+(r/m))^mT

where,

FV = Future Value

PV = Present Value = 4000

r = annual interest rate = 8% = 0.08

T = number of years = 6

m = Number of periods based on compounding frequency = 1

Substituting these in the above formula, we get

FV = 4000*(1+(0.08/1))^(1*6)

FV = 4000*(1.08)^(6)

FV = 4000*1.5869

FV = 6347.50

Therefore, FV = $6347.50

C)10% compounded annually

We know that the Future value formula is given by,

FV = PV*(1+(r/m))^mT

where,

FV = Future Value

PV = Present Value = 4000

r = annual interest rate = 10% = 0.10

T = number of years = 6

m = Number of periods based on compounding frequency = 1

Substituting these in the above formula, we get

FV = 4000*(1+(0.1/1))^(1*6)

FV = 4000*(1.1)^(6)

FV = 4000*1.7716

FV = 7086.24

Therefore, FV = $7086.24

D)10% compounded semiannually

We know that the Future value formula is given by,

FV = PV*(1+(r/m))^mT

where,

FV = Future Value

PV = Present Value = 4000

r = annual interest rate = 10% = 0.10

T = number of years = 6

m = Number of periods based on compounding frequency = 2

Substituting these in the above formula, we get

FV = 4000*(1+(0.1/2))^(2*6)

FV = 4000*(1+0.05)^(12)

FV = 4000*(1.05)^(12)

FV = 4000*(1.7959)

FV = 7183.43

Therefore, FV = $7183.43

E)10% compounded quarterly

We know that the Future value formula is given by,

FV = PV*(1+(r/m))^mT

where,

FV = Future Value

PV = Present Value = 4000

r = annual interest rate = 10% = 0.10

T = number of years = 6

m = Number of periods based on compounding frequency = 4

Substituting these in the above formula, we get

FV = 4000*(1+(0.1/4))^(4*6)

FV = 4000*(1+0.025)^(24)

FV = 4000*(1.025)^(24)

FV = 4000*(1.8087)

FV = 7234.90

Therefore, FV = $7234.90