1. You wish to save $3500 at the end of 5 years by depositing in$200 into...

1. You wish to save $3500 at the end of 5 years by depositing in$200 into your savings account today, $400 in 1 year, $600 in 2 years, $800 in 3 years, and $900 in 4 years. What interest rate must you earn to reach to goal? Express your answers as a percentage. (Enter only numbers and decimals in your response. Round to 2 decimal places.)

2. You deposit $100 into your savings account today, $200 in 1 year, $300 in 2 years. How much will you be able to withdraw at the end of 3 years if the interest rate is 6%? (Enter only numbers and decimals in your response. Round to 2 decimal places.)

Please show how I could enter it into a TI84 calculator and what formula used on paper so I can learn from it. Thanks in advance!

Expert Solution

Q - 1

You will not be able to solve this question on your calculator. On paper also, you will get stuck somewhere in middle. You will be able to solve it completely in excel that also after iteration.

FV of a payment P_t received at the end of period t, at the end of period n = FV_n_{, t} = P_t x (1 + i)^{n - t} where i is the interest rate per period.

Let i be the annual interest rate. Hence, on a piece of paper we are trying to solve this equation:

FV of $200 into your savings account today, $400 in 1 year, $600 in 2 years, $800 in 3 years, and $900 in 4 years over 5 years = $ 3,500

Hence, 200 x (1 + i)^{5 - 0} + 400 x (1 + i)^{5 -
1} + 600 x (1 + i)^{5 - 2} + 800 x (1 + i)^{5 -
3} + 900 x (1 + i)^{5 - 4} = 3,500

Hence, 200(1 + i)⁵ + 400(1 + i)⁴ + 600(1 + i)³ + 800(1 + i)²+ 900(1 + i) = 3,500

Now we will have to use a hit and trial method to get the value if i that satisfies the equation above.

Iteration 1: Put i = 10%; LHS = 3,664
Iteration 2: Put i = 9%; LHS = 3,581
Iteration 3: Put i = 8%: LHS = 3,499

Hence, i = 8%; i.e interest rate you must earn to reach to goal = i = 8.00%

Q - 2

We want to calculate the FV of $100 into your savings account today, $200 in 1 year, $300 in 2 years, over n = 3 years at i = 6%.

Hence, FV = 100 x (1 + 6%)³ + 200 x (1 + 6%)² + 300 x (1 + 6%) = $ 661.82 = amount you will be able to withdraw at the end of 3 years

jeff jeffy answered 1 month ago

Sylvia is considering depositing $600 at the end of each semi-annual period, for 5 years earning...

Sylvia is considering depositing $600 at the end of each semi-annual period, for 5 years earning interest of 8%. She would like to know how large a one-time lump sum deposit she could make, at the same rate, to have the same amount of money after 5 years. Sylvia later decides needs $ 11,000 in 8 years. She has the opportunity to make a one-time investment that will earn 10% compounded quarterly. How much must she invest to reach her...

you plan to save $500 monthly for 2 years earning 5%interest. how much will you end...

you plan to save $500 monthly for 2 years earning 5%interest. how much will you end up with?

You wish to have $200,000 at the end of twenty years. In the last five years,...

You wish to have $200,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.

You wish to have $250,000 at the end of twenty years. In the last five years,...

You wish to have $250,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly?

1. You wish to retire with $5 Million in 45 years. You estimate you will earn...

1. You wish to retire with $5 Million in 45 years. You estimate you will earn 8% on your investments. How much must you invest each year in order to reach your goal?a. Ordinary (1st payment made at the end of the year)b. Due (1st payment made today) 2. You would like to withdraw $60,000 per year during retirement. You expect to live 20 years after you retire at age 65. How much do you need to have saved by...

You decide to save $1,000 at the end of each year for the next20 years....

You decide to save $1,000 at the end of each year for the next 20 years. If your savings earn an annual interest rate of 2%, how much will you have saved up by the end of 20 years? Round to the nearest cent.

If you wish to have $800 in a savings account at the end of 4 years,...

If you wish to have $800 in a savings account at the end of 4 years, and 5% interest will be paid annually, how much should you put into the savings account now?

1. You wish to save up to $135,000 so you can afford to deposit for a...

1. You wish to save up to $135,000 so you can afford to deposit for a house. You plan to set aside $900 at the start of each fortnight. At the moment, your bank is paying interest at a rate of 3.5% p.a. How many years will it take to reach your target deposit amount? Express your answer in years, to four decimal places (do not type the text ‘years’ in your answer). Please include the workings and the formula.

Annuities: 4 questions Q1: -PV: I save $200/year for 20 years at 5%. What is the...

Annuities: 4 questions Q1: -PV: I save $200/year for 20 years at 5%. What is the present value of these savings? Q2: -FV: I save $200/year for 20 years at 5%. How much will I have in 20 years? Q3: -Payment: I want a $ 1 million in 25 years. I can earn 7% annually. How much do I need to save each month? Q4: -Rate: I invest $250,000 and receive $20,000/year for next 20 years, what rate am I...

1 (a) You wish to save money on a regular basis to finance an exotic holiday...

1 (a) You wish to save money on a regular basis to finance an exotic holiday to a country of your choice in five years. You are confident that with sacrifice and discipline, you can force yourself to deposit GHS1,000 annually, at the end of each year of the next five years into a savings account paying 7% annual interest. How much can you raise at the end of the five years? (b) You borrow GHS50,000 at 8% for five...

Question