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Question 1144861: Jack needs $5100 in 6 years from today to buy a holiday. He invests $2300 today. Find the effective annual rate of interest that Jack needs to earn on this amount (as a %, 2 decimal places) in order to reach his goal.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he needs 5100 in 6 years.
he invests 2300 today.
assuming the money is earning interest at an annual compounding rate, the formula becomes:
f = p * (1 + r) ^ 6
f is the future value
p is the present value
r is the interest rate per time period (years in this case)
n is the number of time periods (years in this case).
the formula becomes 5100 = 2300 * (1 + r) ^ 6
divide both sides of this equation by 2300 to get:
5100 / 2300 = (1 + r) ^ 6
take the 6th root of both sides of this equation to get:
(5100 / 2300) ^ (1/6) = 1 + r
subtract 1 from both sides of this equation to get:
(5100 / 2300) 6 (1/6) = 1 = r
solve for r to get:
r = .141932386.
confirm by replacing r in the original equation with that to get:
5100 = 2300 * (1 + .142932386) ^ 6 which becomes 5100 = 5100.
this confirms the interest rate is correct.
.141932386 = 14.1932386%.
round to 2 decimal places and you get 14.19%.
that's your interest rate, as a percent, rounded to 2 decimal places.
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