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Rs.2000 is invested at the end of every month in an account paying interest 6% per year compounded monthly. What is the future value of annuity after 10th payment? (Given that (1.005)10 = 1.0511)?
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Rs.2000 is invested at the end of every month in an account paying int...
Calculation of Future Value of Annuity
Given:
- Amount invested at the end of every month = Rs. 2000
- Interest rate per year = 6%
- Compounding period = Monthly
- Number of payments = 10
- (1.005)^10 = 1.0511
Step 1: Calculation of Monthly Interest Rate
To calculate the monthly interest rate, we need to divide the annual interest rate by the number of compounding periods in a year.
Monthly Interest Rate = (6%/12) = 0.5%
Step 2: Calculation of Future Value of Annuity
Future Value of Annuity (FVA) is the total value of all the payments made at the end of each month compounded at the monthly interest rate for the given number of periods.
Using the formula for FVA:
FVA = [PMT x ((1 + r)^n - 1)]/r
- PMT = Rs. 2000 (Amount invested at the end of every month)
- n = 10 (Number of payments)
- r = 0.5% (Monthly interest rate)
Substituting the values, we get:
FVA = [2000 x ((1.005)^10 - 1)]/0.005
FVA = Rs. 22,937.41
Step 3: Interpretation of Result
The future value of annuity after the 10th payment is Rs. 22,937.41. This means that if Rs. 2000 is invested at the end of every month for 10 months at an interest rate of 6% per year compounded monthly, the total value of the investment at the end of the 10th month would be Rs. 22,937.41.
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Rs.2000 is invested at the end of every month in an account paying int...
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Rs.2000 is invested at the end of every month in an account paying interest 6% per year compounded monthly. What is the future value of annuity after 10th payment? (Given that (1.005)10 = 1.0511)?
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