Your age is 30 years now and you plan to start saving for the retirement that will occur at the age of 60. To accomplish your retirement goals, you intend to save $2,000 at the end of every year until you retire. The first deposit will occur in one year from today and the last deposit will be made when you retire at age 60. Suppose that the retirement fund promises you a return of 8% per year: a) How much will you have saved for the retirement? b) Now assume that you don’t start funding towards your retirement savings instantly. Instead, you wait and start saving from the time you turn 35 years with your first deposit occurring at the end of that year. Calculate the amount saved for the retirement in this scenario. c) Redo part a) assuming that the retirement fund delivers 6% per annum compounded semi-annually.
Question
Your age is 30 years now and you plan to start saving for the retirement that will occur at the age of 60. To accomplish your retirement goals, you intend to save $2,000 at the end of every year until you retire. The first deposit will occur in one year from today and the last deposit will be made when you retire at age 60. Suppose that the retirement fund promises you a return of 8% per year: a) How much will you have saved for the retirement? b) Now assume that you don’t start funding towards your retirement savings instantly. Instead, you wait and start saving from the time you turn 35 years with your first deposit occurring at the end of that year. Calculate the amount saved for the retirement in this scenario. c) Redo part a) assuming that the retirement fund delivers 6% per annum compounded semi-annually.
Solution
a) To calculate how much you will have saved for retirement, we will use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
where:
- P is the annual deposit ($2,000)
- r is the annual interest rate (8% or 0.08)
- n is the number of years (60 - 30 = 30 years)
FV = 2,000 * [10.06 - 1] / 0.08 FV = 226,500
So, you will have saved $226,500 for retirement.
b) If you start saving at 35 instead of 30, the number of years (n) changes to 25 (60 - 35).
FV = 2,000 * [6.84 - 1] / 0.08 FV = 146,000
So, if you start saving at 35, you will have saved $146,000 for retirement.
c) If the retirement fund delivers 6% per annum compounded semi-annually, the interest rate (r) and the number of years (n) both change. The interest rate becomes 3% (6% / 2) and the number of years becomes 60 (30 * 2).
FV = 2,000 * [5.74 - 1] / 0.03 FV = 158,000
So, if the retirement fund delivers 6% per annum compounded semi-annually, you will have saved $158,000 for retirement.
Similar Questions
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