Asahedgeagainstinflation,aninvestorpurchasedanitemin1990forGHS90000and thisitem wassoldintheyear2000forGHS250000.Atwhatinterestdidtheitem appreciateinvalue
Question
Asahedgeagainstinflation,aninvestorpurchasedanitemin1990forGHS90000and thisitem wassoldintheyear2000forGHS250000.Atwhatinterestdidtheitem appreciateinvalue
Solution
To find the interest rate at which the item appreciated in value, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years
In this case, we know: A = GHS 250,000 (the amount the item was sold for in 2000) P = GHS 90,000 (the amount the item was purchased for in 1990) t = 10 years (from 1990 to 2000)
We want to find r, the annual interest rate. We can assume that the interest is compounded once per year (n = 1), which simplifies the formula to:
A = P(1 + r)^t
Rearranging the formula to solve for r gives us:
r = (A/P)^(1/t) - 1
Substituting the known values gives us:
r = (250,000/90,000)^(1/10) - 1
Calculating this gives us:
r ≈ 0.107 or 10.7%
So, the item appreciated in value at an interest rate of approximately 10.7% per year.
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