Question

1) 1 year(s) ago, Youssef had 123,900 dollars in his account. In 4 year(s), he expects to have 299,100 dollars. If he has earned and expects to earn the same return each year from 1 year(s) ago to 4 year(s) from today, then how much does he expect to have in 1 year(s) from today?

2) 2 year(s) ago, Fatima invested 5,690 dollars. In 1 year(s) from today, she expects to have 7,930 dollars. If Fatima expects to earn the same annual return after 1 year(s) from today as the annual rate implied from the past and expected values given in the problem, then in how many years from today does she expect to have exactly 11,710 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

Question 1:

Present Value = $123,900

Future Value = $299,100

n = 5 years

Future Value = Present Value * (1+r)^n

$299,100 = $123,900 * (1+r)^5

(1+r)^5 = 2.41404358

1+r = 1.19274889

r = 0.19274889

r = 19.2749%

Future Value 1 year from today = Investment 1 years ago * (1+r)^n

= $123,900 * (1+19.2749%)^2

= $123,900 * 1.42265018

= $176,266.357

Therefore, value of investment 1 year from today is $176,266.36

Question 2:

Calculation of Annual rate of return

n = 3 years (2 years ago to 1 years from today)

Present Value 2 years ago = $5,690

Value 1 year from today = $7,930

Value 1 year from today = Present Value 2 years ago * (1+r)^n

$7,930 = $5,690 * (1+r)^3

(1+r)^3 = 1.39367311

1+r = 1.11700108

r = 11.7%

Present Value of Investment 2 years ago = $5,690

r = 11.7%

Future Value = $11,710

Future Value = Present value of investment 2 years ago * (1+r)^n

$11,710 = $5,690 * (1+11.7%)^n

(1.117)^n = 2.05799649

n = 6.5225 years

n - 2 = 4.5225

Therefore, it will take 4.52 years to reach $11,710 from today