Your retirement account has a fixed rate of 8% per year paid yearly. You start s

Question

Your retirement account has a fixed rate of 8% per year paid yearly. You start saving for retirement at age 30 with a target retirement age of 65 and $0 in your savings account. Set up and solve a suitable first order differential equation to answer the following questions (compute all interests and payment on a yearly basis).

1. Suppose you set aside $500 every month. How much will you have for your retirement?

2. You want to retire with $500,000. How much should you save every month?

3. Assuming that your salary is going to increase 5% per year during your lifetime you can also decide your contribution should follow suit your monthly contribution increase by 5% every year. If your starting contribution is $500 every month, how much money will you have saved at retirement age?

4. Assuming again that your contribution is increasing by 5% every year, what should your starting contribution be if you want reach $500,000 by retirement age?

Please show steps, thanks!

Explanation / Answer

Retirement Goals Current Savings $0.00 Savings every year $6,000 interest rate factor Factor for 35 years @ 8% (( 1+0.08)^35) 14.78 a. Value of Savings after 35 years $88,680.00 Amount required after 35 years 500000.00 PV Factor for 35 years @ 8% ((1/1.08)^35) 11.645 Amount required to save every year 42936.8828 b.Amount required to save every month 3578.07357 Savings with growth Amount saved every month $500 Amount saved every year $6,000 Increase in contribution every year 5% Interest rate 8% c. Value of savings after 35 years (Future value *(1-(1+g)^35/1+r^35) whole divided by (r-g) 117777.6 where r is rate of interest and g is growth rate (r-g) = (8-5) = 3% Amount required at retirement $500,000 Amonut invested every year 6000 Increase in contribution every year 5% Interest rate 8% d.Starting Amount 306

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.