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A bond has a maturity value of 20,000 Rupees at the end of 4 years. The interest is compounded at the rate of 5% per year.
The initial investment to be made, rounded to the nearest integer, is _______ Rupees.
Correct answer is '16454'. Can you explain this answer?
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Verified Answer
A bond has a maturity value of 20,000 Rupees at the end of 4 years. Th...
Maturity value = 20000
Bond life = 4 years
Interest rate = 5%
Amount of investment to be made can be found from present worth formula = 20000/(1+0.05)^4=16454.04=16454 Rs
Bond life = 4 years
Interest rate = 5%
Amount of investment to be made can be found from present worth formula = 20000/(1+0.05)^4=16454.04=16454 Rs
Most Upvoted Answer
A bond has a maturity value of 20,000 Rupees at the end of 4 years. Th...
Given:
Maturity value (FV) = 20,000 Rupees
Interest rate (r) = 5% per year
Time period (n) = 4 years
To find:
Initial investment (PV) rounded to the nearest integer
Solution:
We can use the formula for compound interest to find the initial investment required:
FV = PV * (1 + r)^n
Where:
FV = Future value (maturity value)
PV = Present value (initial investment)
r = Interest rate per period
n = Number of periods
Step 1: Convert the interest rate to decimal form
The interest rate is given as 5% per year. To use it in the formula, we need to convert it to decimal form by dividing it by 100:
r = 5/100 = 0.05
Step 2: Substitute the given values into the formula
FV = PV * (1 + r)^n
20000 = PV * (1 + 0.05)^4
Step 3: Solve for PV
Divide both sides of the equation by (1 + 0.05)^4:
PV = 20000 / (1 + 0.05)^4
Step 4: Calculate the value of PV using a calculator
PV ≈ 20000 / 1.2155 ≈ 16453.85
Step 5: Round PV to the nearest integer
Rounding PV to the nearest integer gives us the final answer:
PV ≈ 16454 Rupees
Therefore, the initial investment required to have a maturity value of 20,000 Rupees at the end of 4 years with a compounded interest rate of 5% per year is approximately 16454 Rupees.
Maturity value (FV) = 20,000 Rupees
Interest rate (r) = 5% per year
Time period (n) = 4 years
To find:
Initial investment (PV) rounded to the nearest integer
Solution:
We can use the formula for compound interest to find the initial investment required:
FV = PV * (1 + r)^n
Where:
FV = Future value (maturity value)
PV = Present value (initial investment)
r = Interest rate per period
n = Number of periods
Step 1: Convert the interest rate to decimal form
The interest rate is given as 5% per year. To use it in the formula, we need to convert it to decimal form by dividing it by 100:
r = 5/100 = 0.05
Step 2: Substitute the given values into the formula
FV = PV * (1 + r)^n
20000 = PV * (1 + 0.05)^4
Step 3: Solve for PV
Divide both sides of the equation by (1 + 0.05)^4:
PV = 20000 / (1 + 0.05)^4
Step 4: Calculate the value of PV using a calculator
PV ≈ 20000 / 1.2155 ≈ 16453.85
Step 5: Round PV to the nearest integer
Rounding PV to the nearest integer gives us the final answer:
PV ≈ 16454 Rupees
Therefore, the initial investment required to have a maturity value of 20,000 Rupees at the end of 4 years with a compounded interest rate of 5% per year is approximately 16454 Rupees.
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A bond has a maturity value of 20,000 Rupees at the end of 4 years. The interest is compounded at the rate of 5% per year.The initial investment to be made, rounded to the nearest integer, is _______ Rupees.Correct answer is '16454'. Can you explain this answer?
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