Question

An annuity with a cash value of ​$11,200 pays $1,720 at the beginning of every six months. The investment earns 10​% compounded semi-annually.

​(a) How many payments will be​ paid?

​(b) What is the size of the final annuity​ payment

Answer 1

Solution :-

Cash Value = $11,200

Semiannual Interest Rate = 10% / 2 = 5%

Assume the number of Payments be ( n + 1 )

As first payment is beginning of every six months so equation i s

= $11,200 - $1,720 = $1,720 * PVAF ( 5% , n )

$9,480 = $1,720 * [ 1 - ( 1 + 0.05 )^-n ] / 0.05

[ 1 - ( 1 + 0.05 )^-n ] = 0.27558

( 1 + 0.05 )^-n = 0.72442

( 1 + 0.05 )ⁿ = 1.38042

Take log both sides

n log ( 1.05 ) = log ( 1.38042 )

n = 0.1400104 / 0.0211893

n = 6.6076

Therefore Number of Payments = 7.6076

Now Size of Final Annuity = $1,005

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