Question

Calculate the present value of $4,000 received five years from today if your investments pay (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) Present Value 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

Answer:

A = $2,989.30

B = $2,722.33

C = $2,483.68

D = $2,455.65

E = $2,441.08

Explanation:

Given:

Future value (A) = $4,000

Present value (P) = ?

Number of Year (N) = 5.

A. R = 6% = 0.06

$P=\frac{A}{(1+R/100)^N}\\P=\frac{4000}{(1+0.06)^5}\\P=\frac{4000}{(1.06)^5}\\\\P=\frac{4000}{(1.06)^5}\\P=\frac{4000}{1.33822558}\\\\P=2,989.032$

B. R = 8% = 0.08

$P=\frac{A}{(1+R/100)^N}\\P=\frac{4000}{(1+0.08)^5}\\P=\frac{4000}{(1.08)^5}\\\\P=\frac{4000}{1.46932808}\\\\P=2,722.3327$

C. R = 10% = 0.1

$P=\frac{A}{(1+R/100)^N}\\P=\frac{4000}{(1+0.1)^5}\\P=\frac{4000}{(1.1)^5}\\\\P=\frac{4000}{1.61051}\\\\P=2,483.6852$

D. R= 10/2 = 5% N=5*2 = 10

$P=\frac{A}{(1+R/100)^N}\\P=\frac{4000}{(1+0.05)^{10}}\\P=\frac{4000}{(1.05)^{10}}\\\\P=\frac{4000}{1.62889463}\\\\P=2,455.6530$

E. R = 10/4 = 2.5% N = 5*4 = 20

$P=\frac{A}{(1+R/100)^N}\\P=\frac{4000}{(1+0.025)^{20}}\\P=\frac{4000}{(1.025)^{20}}\\\\P=\frac{4000}{1.63861644}\\\\P=2,441.08377$