You are 25 years old and decide to start saving for your retirement - so smart! You plan to save $5,000 each year (so the first deposit will be one year from now), and you will make your last deposit when you retire at age 65. Suppose you earn 8% compounded annually on your retirement savings.
a. How much will you have saved for retirement?
b. How much will you have saved if you wait until age 35 to start saving (again, with your first deposit at the end of the year)?
a. | Saving for retirement | = | Annual cash flow | * | Future value of annuity of 1 | ||
= | $ 5,000.00 | * | 259.0565 | ||||
= | $ 12,95,282.59 | ||||||
Working: | |||||||
Future value of annuity of 1 | = | (((1+i)^n)-1)/i | Where, | ||||
= | (((1+0.08)^40)-1)/0.08 | i | = | 8% | |||
= | 259.0565187 | n | = | 40 | |||
b. | Saving for retirement | = | Annual cash flow | * | Future value of annuity of 1 | ||
= | $ 5,000.00 | * | 113.2832 | ||||
= | $ 5,66,416.06 | ||||||
Working: | |||||||
Future value of annuity of 1 | = | (((1+i)^n)-1)/i | Where, | ||||
= | (((1+0.08)^30)-1)/0.08 | i | = | 8% | |||
= | 113.2832111 | n | = | 30 |
A)
step 1) 65-25= 40
step 2) pv= 5,000* 1/ 0.08* (1-1/ (1+0.08)^40))
5,000* 12.5* 0.9539690667
pv= 59,623.06666875
step 3) 59,623.07* (1+0.08)^40= 1,295,282.6659202
answer:1,295,283
B)
step 1) 65-35= 30
step 2) 5,000* 12.5* (1-1/ (1+0.08)^30)
5,000* 12.5* 0.9006226675
56,288.91671875
step 3) 56,288.92* (1+0.07)^30
566,416.0886165
Answer: 566,416
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