Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $45 000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a superannuation fund. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the superannuation fund earns an annual rate of return of 7%.The future value (FV) at retirement (age 65) of your savings is closest to:
Question
Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $45 000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a superannuation fund. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the superannuation fund earns an annual rate of return of 7%.The future value (FV) at retirement (age 65) of your savings is closest to:
Solution
To solve this problem, we need to calculate the future value of a growing annuity. The formula for the future value of a growing annuity is:
FV = P * [(1 + r)^n - (1 + g)^n] / (r - g)
where:
- P is the first payment (in this case, 8% of the current salary)
- r is the rate of return (7%)
- g is the rate of growth of the payments (5%)
- n is the number of payments (65 - 30 = 35 years)
First, calculate the first payment: P = 3,600
Then, plug the values into the formula:
FV = $3,600 * [(1 + 0.07)^35 - (1 + 0.05)^35] / (0.07 - 0.05)
After calculating the above expression, you will get the future value of your savings at retirement.
Similar Questions
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