Question

You have decided that 20 years after the day you start working full time you will take a leave of absence for avocation around the world. To save money for this vacation, you found an investment that pays 4% nominal interest, compounded annually, and you believe you need $150,000 in that account when you take your trip. You will make end of year deposits every year for the 20 years while working (including the end of your 20th year), and you think your income will increase 2% per year throughout those years. You plan to start your deposits at the end of year 1 with a certain amount of deposit and increase your deposits by 2% each year. How much should you deposit the first year to reach your financial goal for your vacation?

Answer 1

Amount Required for Vacation after 20 years = $150,000

Time Period = 20 years

Interest Rate = 4% annually

Growth Rate of Deposit = 2% per year

Annuity PaymentinGrowing Annuity FV(r-g)/[(1+r)"- (1+g)"]

So,

Amount of Deposit in Year 1 = 150,000(0.04 - 0.02)/[(1.04)²⁰ - (1.02)²⁰]

Amount of Deposit in Year 1 = $4,254.26