Question

1. Your grandmother has invested $4000 in a mutual fund each year on your birthday (she made her first payment when you turned 1 year old). The mutual fund has grown at an annual interest rate of 6.8%. How much is your account worth on the day of your 21^st birthday immediately after your grandmother’s deposit?

answer:

2. You set up a college fund in which you pay $4000 each year at the beginning of the year. How much money (in $) will you have accumulated in the fund after 26 years, if your fund earns 11% compounded annually?

answer:

3. You are planning your retirement and you come to the conclusion that you need to have saved $1000000 million in 30 years. You can invest into an retirement account that guarantees you a 14% annual return. How much do you have to put into your account at the end of each year to reach your retirement goal?

Answer:

Answer 1

1). FV of Annuity = Annual Deposit * [{(1 + r)ⁿ - 1} / r]

= $4,000 * [{(1 + 0.068)²¹ - 1} / 0.068]

= $4,000 * [2.9810 / 0.068]

= $4,000 * 43.8388 = $175,355.17

2). FV of Annuity Due = (1 + r) * Annual Deposit * [{(1 + r)ⁿ - 1} / r]

= (1 + 0.11) * $4,000 * [{(1 + 0.11)²⁶ - 1} / 0.11]

= 1.11 * $4,000 * [14.0799 / 0.11]

= $4,440 * 127.9988 = $568,314.54

3). Annual Deposit = [FV of Annuity * r] / (1 + r)ⁿ - 1]

= [$1,000,000 * 0.14] / [(1 + 0.14)³⁰ - 1]

= $140,000 / 49.9502

= $2,802.79