Question

The value of a stock increases at a rate of 1/2% per year. If the initial value of the stock $40 a share, when will the value of the stock be $50? Round your answer to the nearest tenth of a year

Answer 1

44. 7 yr

Explanation:

The compound interest equation is

`A = P(1+ (r )/( n))^(nt)`

You don't give the frequency of compounding, so I will assume that it is once per year.

Data:

P = $40

r = 0.5 % = 0.005

n =1

Calculations:

(a) Calculate A

A = P + I = 40 + 10 = $50

(b) Calculate t

`50 = 40(1+ (0.005 )/( 1))^(1 * t)\\50 = 40(1+ 0.005)^(t)`

Divide each side by 40

`1.25 = 1.005^(t)`

Take the logarithm of each side

log1.25 = tlog1.005

0.09691 = 0.002 166t

Divide each side by 0.002 166

t = 44.7 yr

The value of the stock will be $50 in 44.7 yr.

Answer 2

After 50 years the stock value will be $50 per share.

Explanation:

Simple Interest Equation (Principal + Interest)

A = P(1 + rt)

Where:

A = Future amont = $50

P = Principal Amount = $40

r = Rate of Interest per year in decimal; r = R/100 = 0.5/100 = 0.005

t = Time Period involved in months or years

Plug in the values

50 = 40(1 + 0.005t)

50 / 40 = (1 + 0.005t)

5/4 = 1 + 0.005t

5/4 - 1 = 0.005t

0.25 = 0.005t

t = 0.25 / 0.005

t = 50 years