Question

You have just turned 26 years of age and accepted your first job.​ however, you would like to retire at 61 years of age. having paid attention in your business​ courses, you have calculated that you will need to save ​$2 million dollars by age 61 to retire comfortably. how much must you put into your retirement savings account each year​ (at the end of the​ year) between now and age 61 ​(assume an interest rate of 6​% ​annually)?

Answer 1

To retire with $2 million at age 61, starting at age 26, a student must save approximately $23,902 annually, assuming a 6% interest rate.

Step-by-step explanation:

In order to calculate how much needs to be saved each year to reach a goal of $2 million by retirement at age 61, we can use the formula for the future value of an annuity. This formula allows us to calculate the regular payments needed when the interest rate and total number of payments are known. The student will need to save for 61 - 26 = 35 years, and with an interest rate of 6%, the annuity payment can be found using the formula P = FV / [(1 + r)^n - 1] / r, where P is the annual payment, FV is the future value (in this case $2 million), r is the interest rate per period, and n is the total number of payments.

The final calculation would be as follows:

P = 2,000,000 / [((1 + 0.06)^35 - 1) / 0.06] = 2,000,000 / [6.02289 - 1) / 0.06] = 2,000,000 / [5.02289 / 0.06] = 2,000,000 / 83.715

Therefore, the student must save approximately $23,902 at the end of each year from age 26 to age 61 to retire comfortably with $2 million.