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What annual payment will discharge a debt of 1025 due in 2 years at the rate of 5% compound interest?
- a)550
- b)551.25
- c)560
- d)560.35
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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What annual payment will discharge a debt of 1025 due in 2 years at th...
Given: Principal amount (P) = 1025, Time (n) = 2 years, Rate of interest (r) = 5%
To calculate the annual payment that will discharge the debt, we need to use the formula for the present value of an annuity:
PV = (A/r) x [1 - (1/(1+r)^n)]
Where PV is the present value of the annuity, A is the annual payment, r is the rate of interest, and n is the number of years.
We know that PV = P = 1025 (since the present value of the annuity should be equal to the principal amount).
Substituting these values in the formula, we get:
1025 = (A/0.05) x [1 - (1/1.05^2)]
Simplifying the expression inside the brackets, we get:
1025 = (A/0.05) x 0.0976
Solving for A, we get:
A = 551.25 (rounded off to two decimal places)
Therefore, the annual payment that will discharge the debt of 1025 due in 2 years at the rate of 5% compound interest is 551.25.
Hence, the correct answer is option B.
To calculate the annual payment that will discharge the debt, we need to use the formula for the present value of an annuity:
PV = (A/r) x [1 - (1/(1+r)^n)]
Where PV is the present value of the annuity, A is the annual payment, r is the rate of interest, and n is the number of years.
We know that PV = P = 1025 (since the present value of the annuity should be equal to the principal amount).
Substituting these values in the formula, we get:
1025 = (A/0.05) x [1 - (1/1.05^2)]
Simplifying the expression inside the brackets, we get:
1025 = (A/0.05) x 0.0976
Solving for A, we get:
A = 551.25 (rounded off to two decimal places)
Therefore, the annual payment that will discharge the debt of 1025 due in 2 years at the rate of 5% compound interest is 551.25.
Hence, the correct answer is option B.
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What annual payment will discharge a debt of 1025 due in 2 years at the rate of 5% compound interest?a)550b)551.25c)560d)560.35e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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