50 years ago X amount of money was deposited at 46 interest

50 years ago, X amount of money was deposited at 4.6% interest rate (compounded yearly). Currently, there is Y amount of money in the account. Now, If we invest Y in a perpetual annuity we can get $24,000 at the end of each year, indefinitely. How much money was deposited originally (i.e., calculate X).

Solution

interest rate = 4.6% , yearly payment = $ 24000

Y = 24000/4.6% = $ 521739.1

X x (1 + 4.6%)⁵⁰ = 521739.1 = Y

X = $ 55064.18