What equal annual amount must be deposited for 10 years in order to provide withdrawals of...

What equal annual amount must be deposited for 10 years in order to provide withdrawals of $200 at the end of the second year and increasing by 25% per year until the end of tenth year? The interest rate is 10% compounded annually.

Expert Solution

ANSWER:

Increase in withdrawals by 25%

YEAR	0	1	2	3	4	5	6	7	8	9	10
WITHDRAWAL			200	250	312.5	390.625	488.28125	610.3515625	762.9394531	953.6743164	1192.092896

Now we will find the present value of this cash flow at 10%

pv = cash flow in year 2(p/f,i,n) + cash flow in year 3(p/f,i,n) + cash flow in year 4(p/f,i,n) + cash flow in year 5(p/f,i,n) + cash flow in year 6(p/f,i,n) + cash flow in year 7(p/f,i,n) + cash flow in year 8(p/f,i,n) + cash flow in year 9(p/f,i,n) + cash flow in year 10(p/f,i,n)

pv = 200(p/f,10%,2) + 250(p/f,10%,3) + 312.5(p/f,10%,4) + 390.625(p/f,10%,5) + 488.28(p/f,10%,6) + 610.35(p/f,10%,7) + 762.93(p/f,10%,8) + 953.67(p/f,10%,9) + 1,192.09(p/f,10%,10)

pv = 200 * 0.8264 + 250 * 0.7513 + 312.5 * 0.683 + 390.625 * 0.6209 + 488.28 * 0.5645 + 610.35 * 0.5132 + 762.93 * 0.4665 + 953.67 * 0.4241 + 1,192.09 * 0.3855

pv = 165.29 + 187.83 + 213.44 + 242.55 + 275.62 + 313.21 + 355.92 + 404.45 + 459.6

pv = 2,617.91

now we will find the annual equivalent amount.

aw = pv(a/p,i,n)

aw = 2,617.91(a/p,10%,10)

aw = 2,617.91 * 0.1627

aw = 426.05

so the annual equal amount that needs to be deposited is $426.05

Rahul Sunny answered 1 month ago

What is the amount of 20 equal annual deposits that can provide 40 annual withdrawals when...

What is the amount of 20 equal annual deposits that can provide 40 annual withdrawals when a first withdrawal of $2,000 is made at the end of year 21 and subsequent withdrawals increase at the rate of 3 % per year over the previous year’s withdrawal. Determine the deposit amounts based on the interest rate of 7 % compounded annually.

What is the amount of six equal annual deposits that can provide ten annual withdrawals, where...

What is the amount of six equal annual deposits that can provide ten annual withdrawals, where a first withdrawal of $22332 is made at the end of year seven and subsequent withdrawals increase at $2092 over the previous year, at an interest rate of 5% compounded annually?

How much must be deposited in an account to have annual withdrawals of $ 2607 forever?...

How much must be deposited in an account to have annual withdrawals of $ 2607 forever? Interest is compounded quarterly and the interest rate is 9% for the first 13 years and 15 % thereafter. The answer is close to

What amount must be deposited in an account that earns 10% on January 1, 2017 if...

What amount must be deposited in an account that earns 10% on January 1, 2017 if an investor wants to withdraw $5,000 January 1 of each year beginning on January 1, 2018 with the last withdrawal being made on January 1, 2021? What if the withdrawals take place on December 31 of each year starting on December 31, 2017 until December 31, 2020? What if withdrawals of $2,500 occur every six months on June 30 and Dec 31 of each...

What sum deposited today at 6% compounded annually for 12 years will provide the same amount...

What sum deposited today at 6% compounded annually for 12 years will provide the same amount as $1300 deposited at the end of each year for 12 years at 8% compounded annually? 1.What sum would have to be deposited today at 6% interest compounded annually? Round to the nearest cent

What is the amount to be deposited at time 0 (zero) so that after 20 years...

What is the amount to be deposited at time 0 (zero) so that after 20 years you can start paying a semiannual term rent of 200 euros each, payable at the beginning of each semester and for the next 25 years, for a fee 7% per year with bimonthly capitalizations in the first 15 years and 4% per semester with quarterly capitalizations in the following years.

You will retire in 40 years. At that time you will begin making annual withdrawals and...

You will retire in 40 years. At that time you will begin making annual withdrawals and the first withdrawal will need to have the purchasing power that $127,849 has today. You will withdraw the same amount of money each year of retirement (and you recognize that its purchasing power will fall as inflation continues). You plan to live for 24 years during retirement, necessitating 24 withdrawals. Inflation equals 6% per year. Obviously, you will need to save (and invest) money...

An amount of $3,000 is deposited into Fund X, which earns an annual effective rate of...

An amount of $3,000 is deposited into Fund X, which earns an annual effective rate of 8%. At the end of each year, the interest earned plus an additional $150 is withdrawn from the fund. At the end of the twentieth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 10%. Determine the accumulated value of Fund Y at the end of year 20. Justify...

John Bautista needs $23,800 in 10 years. Click here to view factor tables What amount must...

John Bautista needs $23,800 in 10 years. Click here to view factor tables What amount must he invest today if his investment earns 12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) Investment at 12% annual interest $ Investment at 12% annual interest, compounded quarterly $

What is the annual equivalent amount at i = 10% for the payment series with the...

What is the annual equivalent amount at i = 10% for the payment series with the first payment in the amount of $2000 in year 2 and the second payment in year 4 at $4000 and the third payment of $6000 in year 6?

Question