Problem Solving (PS) | Hans invested 10,000 at an annual interest rate of x percent, compound

XimeSol

Given: Hans invested 10,000 at an annual interest rate of x percent, compounded annually.

Asked: If the annual interest rate of x percent had been compounded semiannually, how much more interest, in dollars, would he have earned of his 10,000 investment for the first year in terms of x?

Compounded annually: -
Principal P = 10000
Rate of interest = r = x/100
Period of compounding n = 1
A = P (1 + r)^n = 10000 (1 + x/100)^1
Interest = A - P = 10000 (1 + x/100 - 1) = 100x

Compounded semiannually: -
Principal P = 10000
Rate of interest = r = x/200
Period of compounding n = 2
A = P (1 + r)^n = 10000 (1 + x/200)^2
Interest = A - P = 10000 (1 + x/200)^2 - 10000 = 10000 (1 + x^2/40000 + x/100 - 1) = 10000 (x/1000 + x^2/40000)

More interest = 10000 (x/100 + x^2/40000) - 100x = x^2/4

IMO E

Statistics : Posted by Kinshook • on 03 Dec 2023, 12:08 • Replies 3 • Views 131

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