Question

Juan invests $7500 at 6% interest in one year. How much money will he have if the interest were compounded A. yearly B. Daily C. why are the amounts in answers a and b different

Answer 1

Answer:

A) 7,950$, B) 7,963.73$, C) Since daily interest means that 6%/365 of 7500 will be added and compounded every day for the given amount of time(in this case, one year), while annual interest means that 6% of 7500 will be added and compounded yearly for the given amount of time(I'm this case, one year).

Step-by-step explanation:

Given the compound interest formula, A = P(1+r/n)^nt, where A = total amount(final amount), P = principle or amount of money deposited(starting amount), r = annual interest rate(percent interest in respect to t ; decimal = %/100), and n = conversion rate(number of times compounded per t; how much is it compounded)

t = time(time in respect to years ; how long it is compounded).

For A) A = 7500( 1 + 6%/365 ) ^ 365 = 7500(1 + 0.06/365) ^365 = 7500(1 + 0.00016438356..)^365= 7500(≈1.0001644^365) = 7500(100.01644%^365) = 7500(≈106.183%) = 7963.725 ≈ 7963.73$

For B) A = 7500( 1 + 6% ) ^ 1 = 7500(1 + 0.06) = 7500(1.06) = 7500(106%) = 7950$

C) this is because compounding something with a higher frequency leads to a different percentage (as n approaches infinity with time proportional to the annual rate, the ratio between the principle and total amount are proportional to e)