Question

You just graduated and you plan to work for 10 years and then to leave for the Australian “Outback” bush country. You figure you can save $1,155 a year for the first 5 years and $1,944 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $4,983 graduation gift. If you put the gift now, and your future savings, when they start, into an account that pays 9.6% compounded annually, how much will you have when you leave for Australia 10 years from now? (Round answer to 2 decimal places. Do not round intermediate calculations).

Answer 1

There are three parts of savings and we have to calculate the future value (FV) of each separately and then add up them to know the amount 10 years from now

· Saving of $1,155 a year for the first 5 years

· Saving of $1,944 a year for the next 5 years

· A $4,983 of graduation gift

Now calculate the FV of each at the end of year 10

1. Saving of $1,155 a year for the first 5 years

FV = PMT *{(1+i) ^n−1} / i

Where FV =?

PMT = Annual savings = $1,155

Annual interest rate = 9.6% per year

n = N = number of deposits = 5

Therefore,

FV = $1,155 * [(1+9.6%) ^5 -1]/9.6%

FV = $6,995.45 (this is the worth of annul deposits after 5 years but we have to calculate the worth of account at the end of year 10)

We can use following formula to calculate the future value (FV) or worth of the investment

FV = PV * (1+i) ^n

Where,

Present Value PV = $6,995.45 (future value in above calculation is present value in this calculation)

Future value of investment FV after 10 years =?

Annual interest rate i =9.6%

Time period n = 5 years (10 -5 = 5)

Therefore,

FV = $6,995.45 (* (1+ 9.6%) ^5

= $11,062.89

The Future Value of the deposits after the end of 10 years will be $11,062.89

2. Saving of $1,944 a year for the next 5 years

FV = PMT *{(1+i) ^n−1} / i

Where FV =?

PMT = Annual savings = $1,944

Annual interest rate = 9.6% per year

n = N = number of deposits = 5

Therefore,

FV = $1,944 * [(1+9.6%) ^5 -1]/9.6%

FV = $11,774.16

3. A $4,983 of graduation gift

We can use following formula to calculate the future value (FV) or worth of the investment

FV = PV * (1+i) ^n

Where,

Present Value PV = $4,983

Future value of investment FV after 10 years =?

Annual interest rate i =9.6%

Time period n = 10 years

Therefore,

FV = $4,983 * (1+ 9.6%) ^10

= $12,462.25

Now we have to add up the FV values which we have calculated in above 3 parts to know the amount into account 10 years from now when you leave for Australia

Total amount = $11,062.89 + $11,774.16 +$12,462.25 = $35,299.30