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An individual makes rental payments of $1,200(A) per month and wants to know the present value
of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each
month(imm). The current interest rate is 8% per annum?
of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each
month(imm). The current interest rate is 8% per annum?
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An individual makes rental payments of $1,200(A) per month and wants t...
Understanding Present Value of Rental Payments
The present value (PV) of rental payments reflects the current worth of future cash flows, considering a specified interest rate. Here’s how to calculate the present value of monthly rental payments of $1,200 over one year, with payments made at the start of each month.
Monthly Payment Details
- Monthly Payment (A) = $1,200
- Total Payment Period = 12 months
- Annual Interest Rate = 8%
- Monthly Interest Rate = 8% / 12 = 0.6667%
Present Value Formula
For payments made at the beginning of each period, the present value can be calculated using the formula for the present value of an annuity due:
PV = A * [(1 - (1 + r)^-n) / r] * (1 + r)
Where:
- A = Monthly payment
- r = Monthly interest rate
- n = Total number of payments
Calculating Present Value
1. Convert Annual Rate to Monthly:
Monthly Interest Rate (r) = 0.08 / 12 = 0.0066667
2. Substituting Values:
- A = $1,200
- n = 12
- r = 0.0066667
3. Calculate Present Value:
- PV = 1200 * [(1 - (1 + 0.0066667)^-12) / 0.0066667] * (1 + 0.0066667)
4. Final Calculation:
- PV = 1200 * [11.179] * 1.0066667 = $14,014.78 (approximately)
Conclusion
The present value of the annual rental payments of $1,200 made at the start of each month over a year, at an 8% annual interest rate, is approximately $14,014.78. This value indicates the amount that needs to be invested today at the given interest rate to equal the total rental payments over the specified period.
The present value (PV) of rental payments reflects the current worth of future cash flows, considering a specified interest rate. Here’s how to calculate the present value of monthly rental payments of $1,200 over one year, with payments made at the start of each month.
Monthly Payment Details
- Monthly Payment (A) = $1,200
- Total Payment Period = 12 months
- Annual Interest Rate = 8%
- Monthly Interest Rate = 8% / 12 = 0.6667%
Present Value Formula
For payments made at the beginning of each period, the present value can be calculated using the formula for the present value of an annuity due:
PV = A * [(1 - (1 + r)^-n) / r] * (1 + r)
Where:
- A = Monthly payment
- r = Monthly interest rate
- n = Total number of payments
Calculating Present Value
1. Convert Annual Rate to Monthly:
Monthly Interest Rate (r) = 0.08 / 12 = 0.0066667
2. Substituting Values:
- A = $1,200
- n = 12
- r = 0.0066667
3. Calculate Present Value:
- PV = 1200 * [(1 - (1 + 0.0066667)^-12) / 0.0066667] * (1 + 0.0066667)
4. Final Calculation:
- PV = 1200 * [11.179] * 1.0066667 = $14,014.78 (approximately)
Conclusion
The present value of the annual rental payments of $1,200 made at the start of each month over a year, at an 8% annual interest rate, is approximately $14,014.78. This value indicates the amount that needs to be invested today at the given interest rate to equal the total rental payments over the specified period.
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An individual makes rental payments of $1,200(A) per month and wants to know the present value of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each month(imm). The current interest rate is 8% per annum?
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An individual makes rental payments of $1,200(A) per month and wants to know the present value of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each month(imm). The current interest rate is 8% per annum? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An individual makes rental payments of $1,200(A) per month and wants to know the present value of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each month(imm). The current interest rate is 8% per annum? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An individual makes rental payments of $1,200(A) per month and wants to know the present value of their annual rentals over a 12-month (means 1yr)period. The payments are made at the start of each month(imm). The current interest rate is 8% per annum?.
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