Must post first Compound interest may be considered one of t

Must post first. Compound interest may be considered one of the most important topics in real life. It is part of almost every investment we make, car loan, credit card use, etc., including our retirement planning. (a). Find at least one retirement calculator on the Internet and then estimate the amount of savings you will need at your chosen retirement age. Post the web address or source of the retirement calculator used, and explain how you will reach this financial goal. (b). Estimate the amount of upfront investment required to reach $1,000,000 at your chosen retirement age. Use the compound interest formula assuming quarterly compounding at a 5% annual interest rate for each of the years until your chosen retirement age.

Solution

(a). The retirement calculator used is the one available at http://www.calculator.net/retirement-calculator.html

Age now: 25 years

Planned Retirement Age : 65 years

Life Expectacy: 85 years

Expected Social Security Income; $ 1800/Month

Other Income after Reitirement: 0

Average investment Return: 6 %

Annual Inflation Rate: 3 %

Current Incoome: $ 120,000 /Year

Income needed after Retirement: 80 %

Savings required at the time of Reitirement: $ 3,660,080

Life Style after Retirement: Similar to current Lifestyle

77% of income will be from saviungs and 23 % from social security.

(b) The formula for compound interest ( interest compounded quarterly) is M = P(1+r/400)⁴ⁿ , where P is the initial investment, r is the annual rate of interest, and n is the number of years. Here, n = 40, r/400 = 5/400 = 1/80 and M = $ 1000000. Then, we have 1000000= P( 1+1/80)¹⁶⁰ or, P = 1000000/(81/80)³⁶⁰ = 1000000/87.54099514 = $ 11423.22 ( on rounding off to the nearest cent).