Question

1. Semi-annual payments of P500 at the end of each term for 10 years with interest rate of 5% compounded
semi-annually.​

Answer 1

Answer:

1. Semi-annual payments of P500 at the end of each term for 10 years with interest rate of 5% compounded

semi-annually.

Answer 2

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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