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 2 months ago

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