Question

Find the accumulated value of a 10-year annuity-immediate of 100 per year if the first 6 payments are invested at an effective rate of interest of 5% and the final 4 payments are invested at an effective rate of interest of 4%. (Yield curve method)

Answer 1

An annuity immediate is an annuity that is made at the end of the payment period. Basically, it is an ordinary annuity.

1.Accumulated value of $100 for 6 years at 6% effective rate of interest:

Annual investment= $100

Time= 6 years

Interest arte= 6%

The accumulated value at the end of 6 years is calculated by entering the below in a financial calculator:

PMT= 100; N= 6; I/Y= 6

The accumulated value at the end of 6 years is $697.53.

2. Accumulated value of $100 for 4 years at 4% effective rate of interest:

Annual investment= $100

Time= 4 years

Interest rate= 4%

The accumulated value at the end of 6 years is calculated by entering the below in a financial calculator:

PMT= 100; N= 4; I/Y= 4

The accumulated value at the end of 4 years is $424.65.