Calculate Future Value Of 5600 Received Today And Deposit

Calculate Future Value Of 5600 Received Today And Deposit

Calculate the future value of $5,600 received today and deposited at 9 percent for three years. Calculate the present value of $90,000 to be received in 15 years, assuming an opportunity cost of 14%. Calculate the present value of a $10,000 perpetuity at an 8% discount rate. You have obtained a seven-year, 8 percent loan with a bank requiring annual end-of-year payments of $960.43. Calculate the original principal amount. Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6 percent. A deep discount bond can be purchased for $312 and in 20 years it will be worth $1,000. What is the rate of interest on the bond? You have borrowed $25,000 from the bank at 15 percent to be repaid in 10 equal annual installments. Calculate the end-of-year payment.

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Calculate Future Value Of 5600 Received Today And Deposit

Calculate Future Value Of 5600 Received Today And Deposit

The calculation of future value (FV) is a fundamental concept in finance that determines how much an initial sum of money will grow over a specified period at a given interest rate. It helps investors, borrowers, and financial analysts project potential earnings and make informed decisions. In this essay, we examine a series of key financial calculations based on the provided scenarios, including future value, present value, perpetuities, loan amortization, bond valuation, and annuities.

1. Future Value of $5,600 Received Today and Deposited at 9% for Three Years

The future value of a sum received today can be calculated using the compound interest formula: FV = PV × (1 + r)^n, where PV is the present value or initial deposit, r is the annual interest rate, and n is the number of years. Plugging in the values:

  • PV = $5,600
  • r = 0.09
  • n = 3

FV = $5,600 × (1 + 0.09)^3 = $5,600 × 1.295029 = approximately $7,261.61.

2. Present Value of $90,000 to be Received in 15 Years at a 14% Opportunity Cost

Present value (PV) assesses the current worth of a future sum discounted at a specified rate using the formula: PV = FV / (1 + r)^n. Here:

  • FV = $90,000
  • r = 0.14
  • n = 15

PV = $90,000 / (1 + 0.14)^15 = $90,000 / 6.4776 ≈ $13,878.12.

3. Present Value of a $10,000 Perpetuity at 8% Discount Rate

A perpetuity is a perpetual annuity, and its present value is calculated as PV = Payment / r. Here:

  • Payment = $10,000
  • r = 0.08

PV = $10,000 / 0.08 = $125,000.

4. Original Principal Amount of an 8% Loan with Annual Payments of $960.43 over 7 Years

This scenario involves calculating the present value of an annuity to find the initial principal. The formula for the present value of an annuity is:

PV = Pmt × [(1 - (1 + r)^-n) / r]

Where:

  • Pmt = $960.43
  • r = 0.08
  • n = 7

PV = $960.43 × [(1 - (1 + 0.08)^-7) / 0.08] ≈ $960.43 × 5.746 ≈ $5,520.89.

5. Future Value of an $5,000 Annual Annuity Deposited at 6% for Eight Years

Using the future value of an ordinary annuity formula: FV = Pmt × [(1 + r)^n - 1] / r, where:

  • Pmt = $5,000
  • r = 0.06
  • n = 8

FV = $5,000 × [(1 + 0.06)^8 - 1] / 0.06 = $5,000 × (1.593848 - 1) / 0.06 ≈ $5,000 × 9.897 ≈ $49,485.

6. Bond Valuation: Interest Rate Calculation

A deep discount bond purchased at $312 that matures in 20 years worth $1,000 involves solving for the rate of return, or yield to maturity (YTM). The formula relates present value to future value:

$312 = $1,000 / (1 + r)^20

Rearranged to find r:

(1 + r)^20 = $1,000 / $312 ≈ 3.205

r ≈ (3.205)^(1/20) - 1 ≈ 1.059 - 1 ≈ 0.059 or 5.9%.

7. Loan Repayment Calculation for a $25,000 Loan at 15% over 10 Years

This is an amortized loan problem. The annual payment Pmt is calculated with the formula:

Pmt = PV × [r / (1 - (1 + r)^-n)]

Where:

  • PV = $25,000
  • r = 0.15
  • n = 10

Pmt = $25,000 × [0.15 / (1 - (1 + 0.15)^-10)] ≈ $25,000 × 0.1882 ≈ $4,705.20.

Therefore, the end-of-year payment is approximately $4,705.20.

Conclusion

These calculations demonstrate fundamental financial principles used in investment appraisal, loan amortization, bond valuation, and perpetuities. They provide essential tools for finance professionals to assess the value and risks associated with various financial products and decisions. Future research could explore more complex financial scenarios, such as variable interest rates, inflation adjustments, and options strategies, to deepen understanding of financial decision-making.

References

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