Estimating Future Value of Annuity Payment

This document provides step-by-step solutions and examples for estimating the future value of annuity payment using a given formula. It covers topics such as interest rates, EMI calculations, and effective rates. Suitable for Maths students.

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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.

Question 3
Future value = 15000*1.130 = $261,741
Question 4
Let the amount to be invested at the present be $X
Then, X*1.0840 = $400,000
Solving the above, X = $18,412.37
Question 5
The formula for EMI (Equal Monthly Instalment) is shown below.
Here, P=$24,000, R =6% p.a. or (6/12) =0.5% per month, N = 4 years or 48 months
EMI = (24000*0.005*1.00548)/(1.00548-1) = $563.64
Question 6
20000 = 10000*(1.08)N
Solving the above, we get N= 9 years
Question 7
True rate of return =[1+(9/1200)]12-1 = 9.38% per annum
Question 8

The future value of the annuity payment can be estimated using the following formula.
In the given case P =$300, r=10% p.a. or (10/12) = 0.8333% per month, n=25*12= 300
months
Hence, amount after 25 years for the annuity payment = 300*(1.008333300-1)/0.008333=
$398,050
However, there was initial $ 1,000 in the savings account as well.
Thus, total money in the account after 25 years = 398050 + 1000*1.125 = $408,884.7
Question 9
Let the interest rate to be charged be R percent per annum
Then, 2P = P (1+ (R/100))7
Solving the above, we get R = 10.41%
Question 10
Effective rate = (1+(10/1200))12 -1 = 10.47% p.a