Question

Calculate the future value in five years of $6,000 received today if your investments pay (Do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) a. 7 percent compounded annually b. 9 percent compounded annually c. 11 percent compounded annually d. 11 percent compounded semi-annually e. 11 percent compounded quarterly

Answer 1

Future value

= Present value x (1 + r) ^ n

Where,

Present value = $6,000

r = Rate of interest per period

n = Number of periods

When interest is compounded semi-annually , then interest rate is divided by 2 and time is multiplied by 2

When interest is compounded quarterly, then interest is divided by 4 and time is multiplied by 4

a)

Future value

= $6,000 x (1 + 7 / 100) ^ 5

= $6,000 x 1.402552

= $ 8,415.31

b)

Future value

= $6,000 x (1 + 9 / 100) ^ 5

= $6,000 x 1.538624

= $ 9,231.74

c)

Future value

= $6,000 x (1 + 11 / 100) ^ 5

= $6,000 x 1.685058

= $ 10,110.35

d)

Interest rate = 11 / 2 = 5.5% per half year

Time = 5 x 2 = 10 half-years

So, Future value

= $6,000 x (1 + 5.5 / 100) ^ 10

= $6,000 x 1.708144

= $ 10,248.86

e)

Interest rate = 11 / 4 = 2.75% per quarter

Time = 5 x 4 = 20 quarters

So, Future value

= $6,000 x (1 + 2.75 / 100) ^ 20

= $6,000 x 1.720428

= $ 10,322.57