1. Semi-annual payments of P500 at the end of each term for 10 years with interest rate of 5% compounded
semi-annually.
Answers
Answer:
1. Semi-annual payments of P500 at the end of each term for 10 years with interest rate of 5% compounded
semi-annually.
The amount after the end of 10 years is Rs. 12,772.5.
Given: Semi-annual payments of Rs. 500 at the end of each term for 10 years with an interest rate of 5% compounded semi-annually.
To Find: The amount to be received at the end of 10 years.
Solution:
We know that the future value can be calculated by the formula,
FV = P × [(( 1 + r )^n - 1 ) / r ] ....(1)
Where FV = Future Value, P = Regular payments made each term, r = rate of compound interest, n = Number of periods.
Coming to the numerical, we are given;
The regular payments (P) is = Rs. 500
Since, the amount is to be calculated semi-annually, the rate of interest is halved and the number of terms is taken in terms of half years.
The rate of interest (r) = 5 % / 2 = 2.5 %
The number of periods (n) = 10 years = ( 2 × 10 ) half-years
= 20 half-years
Putting the respective values in (1), we get;
F.V = P × [(( 1 + r )^n - 1 ) / r ]
⇒ F.V = 500 × [((( 1 + ( 2.5/100 ))^20 - 1 ) / ( 2.5/100 )]
⇒ F.V = 500 × [(( 1 + 0.025)^20 - 1 ) / 0.025]
⇒ F.V = 500 × [(( 1.025 )^20 - 1 ) / 0.025]
⇒ F.V = 500 × [ 0.6386 / 0.025 ]
⇒ F.V = 500 × 25.545
⇒ F.V = 12,772.5
Hence, the amount after the end of 10 years is Rs. 12,772.5.
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