Financial Calculations and Applications

The assignment content is a series of financial calculations related to loans and savings, including the calculation of monthly payments for a $20,000 loan at 12% interest compounded monthly, quarterly payments for a $120,000 debt at 12% interest compounded quarterly, and equal monthly deposits for a $300,000 fund over 3 years. Additionally, the content includes calculations related to the accumulation of funds over time, including calculations of future values, yearly payments, and principal outstanding after a certain number of payments.

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