Finance Homework: Calculating Future Value, EMI, and Interest Rates

This document presents a comprehensive solution to a finance homework assignment, covering various financial calculations. The solution begins by calculating the future value of an annuity for two different scenarios, demonstrating the impact of investment duration. It then addresses loan options, comparing EMIs with and without interest and rebates. The assignment continues with calculating future values with compound interest, determining the present value needed to reach a future target, and computing EMIs for loans. The document further explores the time required for an investment to double, calculates the true rate of return, and determines the future value of an annuity with an initial deposit. It also involves calculating interest rates and effective rates. The solutions showcase a strong understanding of financial formulas and their practical applications in investment and loan scenarios. This assignment is available on Desklib, a platform offering study resources.

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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