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:
- Set N = 20 (5 years × 4 quarters)
- Set I = 1.2 (annual interest rate)
- Set PV = -520 (cash outflow)
- Set PMT = 0
- Set P/Y = 4 (payments per year)
- 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:
- Set N = 5
- Set PV = -520
- Set FV = 30
- Set PMT = 0
- Set P/Y = 1
- 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.
in finance solver when PMT equals zero compounding periods per year equals payments per year equals
k k is the number of compounding periods per year and a capital N equals n * K there four capital N is the total number
of compounding periods in N years question three Angel has $520 in his saing account Angel
considers investing the money for five years with a bank the bank offers an annual interest rate of
1.2% compounded cly calculate the amount of money Andrew would have at the end of 5 years with a bank give your answer
correct to two decimal places first of all for this question we know PMT equals zero so z y = p y =
k we know this k = 4 n = 5 and r equal 1.2% as long as the PMT equals zero you have two choices either you use
compounding interest formula or use the finance solver it's really up to you I will show you both ways to work
this out I will show you how to use this formula to solve question a future value equals the present value times 1
+ r over 100 * K to the power of 4 K * n then we just need to plug in or do the substitution
520 is a PV so 520 * 1 + 1.2 over 100 * K is 4 4 * 5 then we go to
calculator enter two decimal places $552
111 now I will show you how to use equ solver to solve this question K curly is four so we get
four four and n equals n *
K N is a five so 5 * 4 equals 20
[Music] 1.2% present value is negative 520 PMT is
zero future value is something we are looking for go to menu eight
enter N is a 20 I is 1 2 present value is negative
520 PMT is zero future value is something we are looking for ppy is
four then move the cursor to future value enter we got exactly the same answer
$252 111 instead of investing the money Andrew decides to buy a phone that costs
$520 at the end of five years the phone will have a value of $30 it may be assumed that depreciation
rate per year is a constant find B calculate the annual depreciation rate of the phone this question still
PMT equals zero so if you want to use the finance solver make sure Cy = py = K since PMT
equal zero we can still use this formula to work this out in this situation we need to figure out
depreciation rate per year which means k equal 1 so we do the substitution $30 for future value
present value is 520 1 plus we are looking for this R over 100 *
1 1 * 5 let's let's go to calculator then we go to control menu we want to solve this by equan
solver enter enter enter we got negative answer remember depreciation rate is negative negative
435 at the 36 F by solver R equals 4 43.5 when you answer this question it
should be a positive answer so we will see the depreciation rate is
43.5% do not forget this percentage cypy both one future value is 30 PMT is zero present value is
negative 520 interest rate is something we are looking
for capital N equals NK equal 5 * 1 = 5 let's go to calculator I is something we looking for
present value negative 520 PMT is0 zero future value is a 30 py is
1 move the cursor to I percent enter you got the same answer
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