Lucy recieves a gift of a twenty-one year annuity on the day she was born. the annuity pays $500 on her odd birthday and $700 on even birthday. if the nominal rate of interest is 8% payable monthly, find the value of this annuity on the day she was born. $5,817.13

a few things have me stuck. if the year of her birth time 0 is odd or even. also, i understand i need to consider the interest for 2 years but how to get my monthly nominal to a two year rate. i just did 8% times 2.

Explanation:

Let i represent the nominal annual interest rate (8%). Then the effective annual multiplier of the principal is ...

  (1 +i/12)^12 = (1+.08/12)^12 ≈ 1.0829995

Then the 2-year multiplier is the square of this:

  1+r = (1.0829995)² = 1.1728879

We can use the formula for the present value of an annuity to refer all of the odd-birthday payments to 1 year prior to birth, then adjust by the above annual multiplier. All the even-birthday payments will have the formula applied in the usual way.

  PV = P(1 -(1+r)^-n)/r

where P is the payment amount, (1+r) is the periodic multiplier, and n is the number of payments.

For the odd-birthday payments, the PV (1 year early) is ...

  PV = $500(1 -(1.1728879)^-11/0.1728879 = $2391.5704

so, the amount referred to the day of birth is ...

  1.0829995 × $2391.5704 = $2590.07 . . . . . PV of odd-birthday payments

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The value of even-birthday payments is ...

  PV = $700(1 -(1.1728879)^-10/0.1728879 = $3227.06

And the total value of both sets of payments is ...

  annuity value = $2590.07 +2337.06 = $5817.13

Alternate solution

You could also work this using the PV formula on the sum of ten sets of two years' payments: (700 +500/1.083) and then add the PV of the first odd-year birthday payment: 500/1.083.

This gives ...

  500/1.083 + (700 +500/1.083)(1 -(1.1729^-10))/0.1729 = 5817.13

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

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step-by-step explanation: