Calculate the accumulated value as at 1 january 2021 of...

Calculate the accumulated value as at 1 January 2021 of payments of 100 paid every two years from 1 January 1981 to 1 January 2019 inclusive, using an interest rate of 12% pa effective (solution: 45, 389) Answer must use actuarial notation.

Transcript

00:01 In this question they given here so the payments so which are about the so the january of payments hundred paid every two years from the this january to to the next january so for this we have to calculate the so the future value so the future value so which is at first january so january so january 2 january 2 january 2 2021 so this is what we have to find out so let come to the answer for this question so which is implies that payments are 100 so made every two years so every two years so which is so p mt that is equal to payment frequency so payment frequency and the small m refers to so that every two years so here is the payment frequency the value is so here they give one thousand and small m is equal to here the given that every two years so that we have to take the m value as a two so now number of payments we is equal to so that is n is equal to here last payment year so minus first payment year so which is divided by m plus 1 so from this the n value became n is equal to here so 2019 minus 1981 which is divided by 2 plus 1 so so the n value is is equal to here 38 divided by 2 plus 1 so n value is equal to 20 here so and also they're given in the question that is annual interest rate which is annual interest rate so that is equal to 12 percentage so effective two years rate which is effective two years rate that is small r which is equal to 1 place annual interest rate so which is whole power m minus 1 here so so that small r is equal to 1 place 12 percentage whole power 2 minus 1 so that small r is equal to 1 .25 4 minus 1 so finally small r value is equal to 0 .2 5 double 4 so this is the small add value that is effective two years rate finally now we have to find out the the future value so the future value so at first january so here the first january so 2021 which is given by that is fv is equal to here is fv means value is equal to p m t divided by small r and which is multiply by the one place r whole power n so minus one and this one is multiplied by the one place r here so from the above information we have all done these values in the above particular information that is smaller m and n values now we have to put that values in this formula so let come to that so here which is equal to so hundred divided by 0 .25 double four and multiply by the so 1 plus 0 .25 double for whole power 20 minus 1 which is multiply by so 1 place 0 .25 .25 double 4 so this value became 393 .0 .0.

05:47 817 which is multiplied by so this value became so here 92 .050 and this value is equal to 1 .25 double four so finally after completion of multiplication process of these values so finally this value is 45 ,3886546 so this is the future value.

06:22 So this value we can write as a 45 ,389.

06:30 So why? because this value is nearer to the 89...

Question

Calculate the accumulated value as at 1 January 2021 of payments of 100 paid every two years from 1 January 1981 to 1 January 2019 inclusive, using an interest rate of 12% pa effective (solution: 45, 389) Answer must use actuarial notation.

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