Assignment: Complete The Problems Using An Excel Spreadsheet

Assignment: Complete the problems using an Excel spreadsheet.

Complete the problems using an Excel spreadsheet. Problem responses must contain all givens, equations, and the process in which the problem is solved. What is the amount of interest earned on $6,500 for seven years at 10% simple interest per year? You deposit $10,000 in a savings account that earns 8% simple interest per year. How many years will it take to double your balance?

If, instead, you deposit the $10,000 in another savings account that earns 6% compounded yearly, how many years will it take to double your balance? Suppose you have the option of receiving either $5,000 at the end of five years or P dollars today. Currently, you have no need for the money, so you could deposit the P dollars into a bank account that pays 9% interest compounded annually. What value of P would make you indifferent in your choice between P dollars today and the promise of $5,000 at the end of five years? Which of the following alternatives would you choose, assuming an interest rate of 10% compounded annually?

Receive $400 today. Receive $600 four years from now. Receive $800 eight years from now. State the amount accumulated by a present investment of $4,500 in four years at 7% compounded annually. State the present worth of the future payment of $9,250 six years from now at 9% compounded annually.

Paper For Above instruction

The following analysis addresses several financial problems related to simple and compound interest, using Excel for calculations. Each problem demonstrates understanding of fundamental financial formulas and application of Excel functions for precise computation.

Problem 1: Calculating Simple Interest Earned on an Investment

Given: Principal (P) = $6,500, Time (N) = 7 years, Interest rate (i) = 10% per year

Find: Interest earned (I)

Formula: "I = P × i × N"

Formula with values: "I = 6500 0.10 7"

Solve the problem: =65000.107

Interest earned = $4,550

This calculation illustrates the straightforward application of simple interest formula in Excel, providing an easy way to compute interest over a specified period at a fixed annual rate.

Problem 2: Time Required to Double a Principle with Simple Interest

Given: Principal (P) = $10,000, Rate (i) = 8%

Find: Number of years (N) to double the balance

Formula: "N = (Future Value - Principal) / (Principal i)" or more directly "N = 2" (since doubling the principal means Future Value = 2 P) and using simple interest formula V = P(1 + iN)

Rearranged formula: N = (FV / P - 1) / i

With FV = $20,000, P = $10,000, and i = 0.08, the calculation becomes:

Formula with values: "N = ((2 * 10000) / 10000 - 1) / 0.08"

In Excel, you can write: =(20000/10000 - 1)/0.08

Calculation yields: N = (2 - 1)/0.08 = 12.5 years

This indicates that it will take approximately 12.5 years for the $10,000 to double at 8% simple interest.

Problem 3: Doubling Balance with Compound Interest

Given: Principal (P) = $10,000, Rate (r) = 6% compounded yearly, Future Value (FV) = $20,000

Find: Number of years (N)

Formula: "FV = P(1 + r)^N"

Rearranged for N: "N = log(FV / P) / log(1 + r)"

Formula with values: "N = LOG(20000/10000) / LOG(1 + 0.06)"

Calculation: N = LOG(2) / LOG(1.06)

Using Excel functions: =LOG(20000/10000)/LOG(1+0.06)

Result: N ≈ 11.90 years

This demonstrates how compound interest accelerates growth, requiring approximately 11.9 years to double the balance at 6% annual compounding.

Problem 4: Present Value Indifference at 9% Interest

Given: Future value (FV) = $5,000, Time (N) = 5 years, Rate (i) = 9%

Find: Present value (P)

Formula: "P = FV / (1 + i)^N"

Formula with values: "P = 5000 / (1 + 0.09)^5"

Calculation: =5000 / (1.09^5)

Result: P ≈ $3,346.45

This present value indicates how much should be invested today at 9% to grow to $5,000 in five years, making the decision between receiving $5,000 later or P dollars now equivalent.

Problem 5: Choice with 10% Interest Rate

Alternatives:

  • Receive $400 today
  • Receive $600 in four years
  • Receive $800 in eight years

Calculate the present value of each future amount at 10% interest for a fair comparison:

For $600 in four years: "PV = FV / (1 + i)^N" → =600 / (1.10^4) ≈ $410.65

For $800 in eight years: =800 / (1.10^8) ≈ $367.88

Comparing present values, $400 today has a higher value than the other two options, thus favoring taking $400 now if the decision is solely based on present worth at 10% interest.

Problem 6: Future Value of an Investment

Given: Present investment = $4,500, Rate (r) = 7%, Time (N) = 4 years

Find: Future value (FV)

Formula: "FV = P × (1 + r)^N"

Formula with values: "FV = 4500 * (1 + 0.07)^4"

Calculation: =4500 * (1.07^4)

Result: FV ≈ $6,938.61

This calculation demonstrates the growth of an investment over four years compounded annually at 7%, useful for planning investments.

Problem 7: Present Worth of Future Payment

Given: Future payment (FV) = $9,250, Time (N) = 6 years, Rate (i) = 9%

Find: Present worth (PV)

Formula: "PV = FV / (1 + i)^N"

Formula with values: "PV = 9250 / (1 + 0.09)^6"

Calculation: =9250 / (1.09^6)

Result: PV ≈ $5,950.34

This shows the current value of a future payment, critical for financial planning and investment assessment.

Concluding Remarks

These problems demonstrate the practical application of financial formulas—simple interest, compound interest, present value, and future value—using Excel for precise and efficient computation. Mastery of these calculations is vital for sound financial decision-making, emphasizing the importance of understanding the time value of money in both personal finance and corporate contexts.

References

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