Problema Solution
when P dollars is invested at an annual interest rate r compound once a year, the balance, A, after 2 years is given by A=P91+r)^2
Evaluate A when r=0, and interpret the answer in practical terms
If r is between 5% and 6 %, what can conclude about the percentage growth after 2 years?
Express r as a function of A. Under what circumstances might this function be useful?
What interest rate is necessary to obtain an increase of 25% in 2 years?
Answer provided by our tutors
A=P(1+r)^2
Evaluate A when r=0, and interpret the answer in practical terms:
A =P(1 + 0)^2
A = P
If the interest rate is 0% there will be no change in the balance.
If r is between 5% and 6 %, what can conclude about the percentage growth after 2 years?
0.05 <= r <= 0.06, where r is expressed as a decimal
P(1+0.05)^2 <= P(1 + r)^2 <= P(1+0.06)^2
1.1025P <= A < = 1.1236P
The percentage growth is between: (1.1025P - P)/100 and (1.1236P - P)/100 or between 0.1025 and 0.1236 (between 10.25% and 12.36%).
Express r as a function of A. Under what circumstances might this function be useful?
A=P(1+r)^2
(1+r)^2 = A/P
r = √(A/P) - 1
What interest rate is necessary to obtain an increase of 25% in 2 years?
A = 1.25P
1.25 = P(1 + r)^2
r = √(A/P) - 1
r = √(1.25P/P) - 1
r = √1.25 - 1
r = 0.1180 or 11.80%
Interest of 11.80% is necessary to obtain increase of 25% in 2 years.