Question

"You plan to start saving for your retirement by depositing $9,583 exactly one year from now. Each year you intend to increase your retirement deposit by 3%. You plan on retiring 30 years from now, and you will receive 6% interest compounded annually. This type of cash flow is called a geometric gradient. The formula to calculate the present worth of a geometric gradient is found in Table 3.6 in the textbook.
However, in year 10, you have sudden expenses, and you could not deposit any money at the end of year 10. All of your other deposits remain identical to what you would have deposited if you had not skipped a year. In other words, you still deposit $12,879 at the end of year 11. How much money will you have in your retirement account at the end of 30 years?"

Answer 1

Soltuion :-

The amount at the time of retirement after 30 years if started to deposit after 1 year is

1st installment = $9583

Growth = 3%

Rate of return = 6%

The amount in case of growth Annuity can be calculated by using formula

= 9583 {(1+0.06)²⁹ - (1+0.03)²⁹} / {0.06-0.03}

= 9583 { 5.42 - 2.36 ) / 0.03

= 9583*3.06/0.03

= 977466 $

If the Installment of year 10 is not deposited then the amount is

The money deposit in year 10 is

= Y11 / (1.03) = 12879/1.03 = 12504$

The Future value of amount 12504 at the end of year 30 is =

12504 (1 + 0.06 )²⁰ = 12504 * 3.21 = 40137.47

Therefore the net amount at the time of retirement is 977466 - 40137.47 = 937328.53 $

answered by: anonymous