Question

Find the amount to which $675 will grow under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent. 6% compounded annually for 5 years. $ 6% compounded semiannually for 5 years. $ 6% compounded quarterly for 5 years. $ 6% compounded monthly for 5 years.

Answer 1

Answer:

a) $903.3

b) $907.14

c) $909.13

d) $910.47

Explanation:

Data provided in the question:

Principle amount = $675

Now,

Future value = $(1 +\frac{r}{n})^{n\times t}$

here,

n is the number of periods

r is the Annual rate of interest

t is the time in years

Thus,

a) For 6% compounded annually for 5 years

r = 6% = 0.06

n = 1

t = 5

Future value = $675 × $(1 +\frac{0.06}{1})^{1\times 5}$

or

Future value = $675 × 1.338226

or

Future value = $903.3

b) For 6% compounded semiannually for 5 years

r = 6% = 0.06

n = 2

t = 5

Future value =  $675 × $(1 +\frac{0.06}{2})^{2\times 5}$

or

Future value = $675 × 1.343916

or

Future value = $907.14

c) For 6% compounded quarterly for 5 years

r = 6% = 0.06

n = 4

t = 5

Future value = $675 × $(1 +\frac{0.06}{4})^{4\times 5}$

or

Future value = $675 × 1.346855

or

Future value = $909.13

d) For 6% compounded monthly for 5 years

r = 6% = 0.06

n = 12

t = 5

Future value = $675 × $(1 +\frac{0.06}{12})^{12\times 5}$

or

Future value = $675 × 1.34885

or

Future value = $910.47