Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / You and your statistics-major friend are curious how much rate of returns and compounding impacts an investment over the course of someone’s career
You and your statistics-major friend are curious how much rate of returns and compounding impacts an investment over the course of someone’s career. What is the difference in retirement savings if you invest $100 at the end of each month and earn a 8% return (compounded monthly), and if you invested $1,200 at the end of each year and earned 7% (compounded annually)? Both are for a duration of 50 years.
$274,458
$298,476
$301,478
$305,338
$253,436
| Step1 : | Future value of monthly compounding annuity | |||
| Future Value of an Ordinary Annuity | ||||
| = C*[(1+i)^n-1]/i | ||||
| Where, | ||||
| C= Cash Flow per period | ||||
| i = interest rate per period =8%/12 =0.666667% | ||||
| n=number of period =50*12 =600 | ||||
| = $100[ (1+0.006666667)^600 -1] /0.006666667 | ||||
| = $100[ (1.006666667)^600 -1] /0.006666667 | ||||
| = $100[ (53.8782 -1] /0.006666667] | ||||
| = $793,172.87 | ||||
| Step 2 : | Future value of annual compounding annuity | |||
| Future Value of an Ordinary Annuity | ||||
| = C*[(1+i)^n-1]/i | ||||
| Where, | ||||
| C= Cash Flow per period | ||||
| i = interest rate per period | ||||
| n=number of period | ||||
| = $1200[ (1+0.07)^50 -1] /0.07 | ||||
| = $1200[ (1.07)^50 -1] /0.07 | ||||
| = $1200[ (29.457 -1] /0.07] | ||||
| = $487,834.72 | ||||
| Step 3 : | Difference =$793172.87-487834.72 | |||
| = $305338 | ||||
