Question

Ray is 27 years old today. He is a conservative person, and is thinking about his retirement when he reaches the age of 70. He decides to invest $7,000 at regular annual intervals for 15 years, starting from today. The fund that he is investing in will give him a return of 7.4% per annum. He will then leave the money in the account to grow further until he retires when he is 70 years old. How much will Ray have in the fund when he turns 70?

Select one:

a. $1,544,583

b. $1,601,020

c. $1,438,159

d. $1,319,778

Answer 1

Ray is 27 years old who is investing $7000 per annum starting today for 15 years. After that, that money will grow until he is 70 years. Thus, we need to calculate the following amounts:

Part 1. Amount accumulated at the end of 15 years by investing $7000 per annum at 7.4%

Part 2. The above amount will grow for 28 years. Why 28? Because, he will invest for 15 years from 27 years ie. until 42 years of age. After that the money will have 28 years (70-42) to grow.

Part 1 can be answered using Future value of annuity due which is as following:

where A = $7000, r =0.074(7.4%) & t = 15

Substituting the values in the formula:

Now, this is amount that will grow for further 28 years, which is the 2nd part:

194,844.05 will compound for 28 years at the rate of 7.4% like this:

Option C ($1,438,159) is the answer.