It takes Hiroshi 30 years to reach his investment goal.
The formula for calculating the amount received on the principal amount (P) after t years at r% rate of interest is-
Amount = P(1 + r/100)^t
Let the principle amount with Hiroshi be P
then, the amount that Giulio starts with = 3P
Let time period for Giulio's investment = t
Then, the time period for Hiroshi's investment = 5t
Rate = 5%
As the investment goals of both the people are equal, they will get the same amount.
Therefore, we get the following equation-
P(1 + 20/100)^5t/4 = 3P(1 + 20/100)^t/4
(1 + 20/100)^5t/4 = 3(1 + 20/100)^t/4
[(1 + 20/100)^5t/4] /[(1 + 20/100)^t/4] = 3
(1 + 20/100)^(5t/4- t/4) = 3
(1 + 20/100)^(4t/4) = 3
(1 +0.2)^t = 3
(1.2)^t = 3
Taking log on both sides-
Log (1.2)^t = log 3
t log 1.2 = log 3
t = log 3/ log 1.2
t = 6.025
Time taken by Hiroshi to reach his investment goal = 5t
= 5(6.025)
= 30.128
Thus, it takes Hiroshi 30 years to reach his investment goal.
Learn more about compound interest here-
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