Financial Calculations Assignment: Loans, Investments, and Returns

This document presents the solutions to a finance homework assignment, focusing on various financial calculations. The assignment includes problems on calculating monthly payments for a loan with compound interest, determining quarterly payments for a debt, and calculating the amount of equal monthly deposits needed to reach a future value goal. It also covers scenarios involving different interest rates and time periods for investments, including the calculation of yearly payments under different interest rate scenarios and the growth of funds over time. The solutions demonstrate the application of financial formulas for present and future value, and the calculation of loan amortization schedules. This assignment provides practical examples of financial planning and investment strategies.

Question 1
Amount borrowed = $20,000
Rate of interest = 12 % p.a. compounded monthly
Monthly payments = Amount borrowed x rate (1+ rate)n / (1+r)n-1
Where, rate = monthly rate of interest = 12 % / 12 = 1 %
n= no. of months
Now Monthly payments = 20000 x 1 % (1+ 0.01)8 / (1+0.01)8- 1
=200 x 1.082857 / 1.082857-1
=216.5713 / 0.082857
= $ 2613.806
Question 2
Amount of debt = $ 120,000
To be repaid by quarterly payments for next 3 years
Rate of interest = 12 % p.a. compounded quarterly
a) Quarterly payment = Amount borrowed x rate / 1- (1+ rate)-n
Where,
Rate = quarterly rate of interest = 12/4 = 3 %
N= no. of quarters
Now quarterly payment = 120000 x 3% / 1- (1+.03)-12
= 3600 / 1- 0.70138
= $ 12055.45
b) Calculation of principal outstanding after 8 quarterly payments
= 12055.45[1- (1.03)-4] / 0.03
= 12055.45[1-0.888487] / 0.03
= 12055.45 x 0.111513 / 0.03
= 1344.339 / 0.03
= $ 44811.29

Question 3
Amount needed = $ 300,000
Time = 3 years
Rate = 12 % p.a. compounded monthly
a) 36 equal monthly deposits with first deposit made immediately
Let the amount of deposit be Y
Future value = Y x [(1+ rate)n- 1] x (1+rate) / rate
Where,
Rate= monthly rate = 12 / 12 = 1 %
N= no. of months = 12 x 3 = 36
Now,
300,000 = {Y x [(1+ 0.01)36-1] (1+0.01)} / 0.01
300,000= {Y x [1.430769-1] x 1.01} / 0.01
300,000 = {Y x 0.430769 x 1.01} / 0.01
300,000 = {Y x 0.435076} / 0.01
Y = $ 6895.34
b) 36 equal monthly deposits with first deposit made in 7 months’ time
Let the amount of deposit be Y
300000 = Y [(1+0.01)30 – 1] / 0.01
300000 = Y[1.347849 – 1] / 0.01
Y = $ 8624.43
Question 5
Amount required in the fund at end of 10 years = $ 30,000
Rate of interest (R1) = 8%, Rate of interest (R2) = 9 %
Calculation of yearly payment under R1
=Future value x R1 / [(1+R1)n – 1]

= 30000 x 8 % / [(1+0.08)10-1]
= 2400 / 2.158925-1
= $ 2070.88
Calculation of amount in fund till fourth deposit
= 2070.88 [(1+0.08)4-1] / 0.08
= 2070.88 [1.360489-1] / 0.08
= $ 9331.62
Calculation of yearly payment under R2
This amount will grow at 9 % for remaining 6 years
So amount becomes, 9331.62 x (1.09)6= $ 15650.06
Additional amount needed to be added in fund over 6 years
= 30000 – 15650.66 = $ 14349.94
So yearly payment to fund after 4 years
= 14349.94 x 9 % / (1+0.09)6 – 1
= 1291.495 / 1.6771 – 1
= 1291.495 / 0.6771
= $ 1907.39