Question

You have always dreamed “seeing the world”, and are making plans to do so. You estimate that it will cost about J$1,800,000 for air fares, hotel accommodation, and sight-seeing, and could be done in a six week period. You plan to take this trip in seven year’s time, starting during your pre-retirement leave in January 2018. You intend to start building this travel fund in January 2011, and will continue until December 2017.

1. Your plan is to invest your entire Christmas bonus every year starting January 1, 2011. You estimate that your Christmas bonus will be $80,000 this year, and will increase by 5% per year after that. Every January until 2017 you plan to open a new certificate of deposit with the entire bonus. You don’t intend to withdraw any of these funds until the end of December 2017. What will be the total amount in these accounts in December 2017, if the average expected return on each account is 12% per year?                                                                                                                                            

You also intend to have a monthly savings plan, starting at the beginning of January 2011. Into this account, you plan to put $5,000 at the start of every month, with your final deposit being at the beginning of December 2017. If the average expected interest rate is 12% per year, compounded monthly, how much do you expect to have in the account at the end of December 2017?                                                                                               

Answer 1

Part 1)

The future value of a growing annuity due (since payments are made at the start of year) can be calculated with the use of following formula:

Future Value of Growing Annuity Due = Initial Payment*[((1+Rate of Interest)^Period - (1+Growth Rate)^Period))/(Rate of Interest - Growth Rate)]*(1+Growth Rate)

Here, Initial Payment = J$80,000, Rate of Interest = 12%, Growth Rate = 5% and Period = 7 Years

Using these values in the above formula, we get,

Total Amount at December 2017 = 80,000*[((1+12%)^7 - (1+5%)^7)/(12%-5%)]*(1+5%) = J$1,028,583.66

_____

Part 2)

The future value of annuity due (since payments are made at the start of each month) can be derived as below:

Future Value of Annuity Due = Periodic Payment*[((1+Rate of Interest)^Period - 1)/Rate of Interest]*(1+Rate of Interest)

Here, Periodic Payment = $5,000, Rate of Interest = 12%/12 = 1%, and Period = 7*12 = 84 months [we take 12 since the compounding is monthly]

Using these values in the above formula, we get,

Amount in Account at December 2017 = 5,000*[((1+1%)^84 - 1)/1%]*(1+1%) = J$659,895