# A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually, annual rate of interest 1.8%, compounded quarterly....

A man has $100 and decides to invest it in a bank for 6 years. The bank gives him two choices, annual rate of interest 2%, compounded annually, annual rate of interest 1.8%, compounded quarterly. Which option is better for him?

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Interest is paid on the principal amount deposited at the interest rate fixed by the bank. If interest is being compounded annually, after every one year, the interest earned is added to the initial deposit and interest is now paid on the entire amount. If interest is compounded quarterly, after every quarter, the interest earned is added to the initial deposit and further interest is earned on the entire amount.

If the annual rate of interest is R, the quarterly rate of interest is R/4. The formula that is used to determine interest earned on an amount P, deposited for N years when the rate of interest is R and compounding is done t times in a year is I = P*((1+R/t)^(N*t) - 1)

In the problem the person is given two choices. Determine the interest earned in both the cases.

When he is given interest at 2% per year and compounding is done annually, the interest earned in 6 years is 100*((1+0.02)^6 - 1) = 12.62

When he is given interest at 1.8% per year and compounding is done quarterly, the interest earned is 100*((1+0.018/4)^(6*4) - 1) = 11.38

As the person gets more in terms of interest in the first option, he shouldÂ deposit the $100 at a rate of 2% compounded annually.