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Annuity 1 - This annuity has 6 semi-annual payments in advance which grow at 2% every...

Annuity 1 - This annuity has 6 semi-annual payments in advance which grow at 2% every 6 months. The first payment is $500. The value of this annuity today is:

Annuity 2 - This annuity pays $250 every month for 1 year. The value of this annuity today is:

You are offered $3,000 to sell any one of the investments. Which investment will you sell (if any) and calculate the gain? Answer

Discount rate is 6%p.a

Expert Solution

Answer to question:

Value of annuity = C * [(1+i)n-1]

i

Annuity 1 : Payment =$500 per 6 months

Growth is 2% per 6 months

Value of annuity today is the present value of Annuity

Annuity 1:

C=$500

I=2%

Value of annuity today is = $500*[(1.02)5-1]

.02

=$3,154

Value of annuity today is Present value of $3,154 discounting @6% p.a.

=$3154/(1.06)3

=$2,648

Annuity 2 : $250 per month

Therefore value of annuity is 250*12 =$3000

Present value of annuity = $3000/(1.06)

= $2830

In the given case if I was offered $3,000 to sell any one of the annuity then I will sell annuity 1, because on selling annuity 1 profit is more as compared to profit on selling of annuity 2

Gain on selling of annuity 1

= Amount received on sell of annuity – present value of annuity

= $3000 – 2648

=$352

jeff jeffy answered 1 year ago

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