Calculating Compound Interest and Depreciation Using Finance Solver

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Understanding Key Financial Concepts

  • PMT = 0: No periodic payments are made during the investment or depreciation period.
  • K (Compounding Periods per Year): Number of times interest is compounded annually.
  • N (Total Compounding Periods): Calculated as n (years) multiplied by K.

Question 1: Calculating Future Value with Compound Interest

Angel invests $520 for 5 years at an annual interest rate of 1.2%, compounded quarterly (K=4).

Using the Compound Interest Formula

The formula for future value (FV) when PMT = 0 is:

[ FV = PV \times \left(1 + \frac{r}{100 \times K}\right)^{K \times n} ]

Where:

  • PV = Present Value ($520)
  • r = Annual interest rate (1.2%)
  • K = Compounding periods per year (4)
  • n = Number of years (5)

Substituting values:

[ FV = 520 \times \left(1 + \frac{1.2}{100 \times 4}\right)^{4 \times 5} = 520 \times (1 + 0.003)^{20} ]

Calculating gives:

[ FV \approx 552.11 ]

Using Finance Solver

Steps:

  1. Set N = 20 (5 years × 4 quarters)
  2. Set I = 1.2 (annual interest rate)
  3. Set PV = -520 (cash outflow)
  4. Set PMT = 0
  5. Set P/Y = 4 (payments per year)
  6. Compute FV

Result: $552.11, matching the formula calculation.

Question 2: Calculating Annual Depreciation Rate

Angel buys a phone for $520, which depreciates to $30 after 5 years. The depreciation rate is constant annually.

Using the Depreciation Formula

The formula is similar to compound interest but solving for r:

[ FV = PV \times (1 + \frac{r}{100} )^{n} ]

Given:

  • FV = $30
  • PV = $520
  • n = 5

Rearranged to solve for r:

[ r = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1 ]

Using finance solver:

  1. Set N = 5
  2. Set PV = -520
  3. Set FV = 30
  4. Set PMT = 0
  5. Set P/Y = 1
  6. Compute I (interest rate, which is depreciation rate here)

Result: Approximately 43.5% annual depreciation rate.

Summary

  • When PMT = 0, use either the compound interest formula or finance solver for calculations.
  • For compound interest, adjust K and N according to compounding frequency and years.
  • For depreciation, treat the rate as a negative growth rate and solve accordingly.
  • Finance solver provides consistent results with manual formula calculations.

This approach ensures accurate financial computations for investments and asset depreciation.

For more detailed insights on related financial calculations, check out our guides on Calculating Loan Outstanding Balance Using Present Value Method and Understanding Depreciation and Tax Liability Calculations for Assessment Year 2021-22. Additionally, if you're interested in understanding how to calculate profits, you might find our article on Calculating Profits Using Arithmetic and Geometric Sequences helpful.

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