Future Interest compounded monthly???

Question

At 25 Jonas Grumbly began making monthly deposits of $345 a month into an annuity that earns 6.7% compounded monthly for a period of 20 years. After turning 45, he stopped making monthly payments and the money in the account continued to earn 6.7% compounded monthly until he retired at the age of 70. How much money was in the account when he turned 45?

Answer 1

At age 25, Jonas ads $345 dollars every month into the annuity until 20 years later at 45. 20 years * 12 months/year = 240 months total. In addition, the value of the annuity is appreciated by 6.7% compounded monthly for 240 months.

In the next phase of the annuity, no money is added but the amount continues to appreciate at the same rate for 25 years or 25 * 12 months/year = 300 months.

However the question asks, how much money was in the account when he turned 45 so we can ignore the second phase.

The equation for determining the future value of an annuity given the periodic payments, period rate and number of periods is:

F = P[((1+r)^n - 1)/r], where P = annual payment, r = the rate per period and n = the number of periods.

Plugging in r = 0.067, n = 240 and P = 345 will give the answer.