Question

an annuity pays 3 at the beginning of each 3 year period for 30 years. Find the Accumulated value of the annuity just after the final payment, using i(2)=0.06

Answer 1

Solution :-

Interest Rate Annually = ( 1 + 0.06 / 2 )² - 1 = 1.0609 - 1 = 0.0609 = 6.09%

Now Interest Rate of 3 Years = ( 1 + 0.0609 )³ - 1 = 1.19405 - 1 = 0.19405 = 19.405%

Now For the Future Accumulated Value we need to take n = 30 / 3 = 10

As We use interest rate of 3 Years

Now the Accumulated Value after 27 Years ( as final payment is in 27 years =

= $3,000 * FVAF ( 19.405% , 10 ) *

= $3,000 * [ ( 1 + 0.19405 )¹⁰ - 1 ] / 0.19405

= $15,459.75 * [ 5.8916 - 1 ]

= $75,622.76

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