Estimating Future Value of Annuity Payment

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Question 1
The future value of the annuity payment can be estimated using the following formula.
(A) For this case, P = $2,500, r = 9% p.a. n= 65-45= 20 years
Hence, account balance at the age of 65 years = 2500*(1.0920-1)/0.09 = $127,900.3
(B) For this case, P = $2,500, r = 9% p.a. n= 65-21= 44 years
Hence, account balance at the age of 65 years = 2500*(1.0944-1)/0.09 = $1,203,804.44
Question 2
(a)Option 1: No interest is levied under this option
Hence, EMI = (34875-3500)/72 = $435.77
Option 2: Interest of 3.49% would be applicable but a rebate of $ 5,000 would be available
Hence, principal = 34875-3500-5000 = $29,875
The EMI can be computed using the following formula.
Here, P=$29,875 R =3.49% p.a. or (3.49/12) =0.2908% per month, N = 72 months
EMI = (29875*0.002908*1.00290872)/(1.00290872-1) = $460.49
(b)It is evident that Option 1 offers the lowest payment.