If you put 1000 in a bank account with an APY of 56 and Bill

If you put $1000 in a bank account with an APY of 5.6% and Bill Gates puts $1,000,000,00 into a bank account that has an APY of 2.1%, when will you have more money than Bill Gates? Also, how much money would you have at that point in time?

Solution

solution-

assuming APY is applied annually then annual product yield = (1+r/n)ⁿ-1 = r as n equal to 1

hence apy= nominal interest rate r

using compound interest formula

given condition

my money after n years>money of bill gates

1000(1+r₁100)ⁿ>100000000(1+r₂/100)ⁿ

where r₁=5.6 and r₂=2.1

applying this and finding the value of n

[(1+0.056)/(1+0.013)]ⁿ>100000

1.042ⁿ>10⁵

from this inequality we can find n

so for that value of n

my amount is 1000(1+0.056)ⁿ