Question

2 year(s) ago, Pablo had 235,800 dollars in his account. In 6 year(s), he expects to have 426,000 dollars. If he has earned and expects to earn the same return each year from 2 year(s) ago to 6 year(s) from today, then how much does he expect to have in 1 year(s) from today?

3 year(s) ago, Fatima invested 6,100 dollars. In 2 year(s) from today, she expects to have 8,660 dollars. If Fatima expects to earn the same annual return after 2 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 11,190 dollars? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Answer 1

a.

The rate of return earned by Pablo in 8 years is calculated below:

235, 800 X (1+i) = 426,000

9908'1 = (2+1)

(1+i) = 1.80665

(1+i) = 1.0767335

i=0,0767335

The expected amount in 1 year is calculated below:

Account balance = 235,800 X (1+0.0767335)

Account balance = 294, 353.01

b.

The rate of return earned by Fatima in 5 years is calculated below:

6, 100 X (1+i) = 8,660

(1+i) = 1.419672

$9908'T = (?+I)

(1+i) = 1.0726

i = 0,0726

The number of years in which account reaches to 11,190 is calculated below:

6, 100 x (1 +0.0726) = 11,190

(1.0726) = 1.834426

Take log on both sides

nlog (1.0726) = log1.834426

log1.834426 log (1.0726)

n = 8,657

So, number of years from today is (8.657 - 3) = 5.657.