Asahedgeagainstinflation,aninvestorpurchasedanitemin1990forGHS90000and thisitem wassoldintheyear2000forGHS250000.Atwhatinterestdidtheitem appreciateinvalue
Question
As a hedge against inflation, an investor purchased an item in 1990 for GHS 90,000 and this item was sold in the year 2000 for GHS 250,000.
At what interest did the item appreciate in value?
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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