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Suppose you want to have $500,000 for retirement in 30 years. Your retirement account earns 4% interest compounded monthly. A, how much would you need to deposit in the account each month and b, how much interest would you earn over the 30 years? To answer this question we will use the annuity formula shown here below where A is the account balance after two years, PMT is the regular deposit amount, r is the annual interest rate as a decimal, n is the number of compounds per year, and t is the time in years. Because you want $500,000 in the account after 30 years, A is $500,000. This must be equal to the regular payment or PMT. And then we have times, and then in parentheses we have one plus r divided by n raised to the power of nt and then minus one. So we have one plus r is equal to 4% which as a decimal is 0.04, which is divided by n. Because the interest is compounded monthly and there are 12 months a year, n is 12. And this is raised to the power of n times two which is 12 times,
