Financial Math Assignment: Annuities, Mortgages, and Loan Calculations

This document provides solutions to a financial math assignment covering various concepts related to annuities, mortgages, and loan calculations. The assignment includes problems involving loan repayment calculations, determining monthly payments for mortgages, calculating total interest paid on loans, and analyzing the impact of different interest rates and payment terms. The solutions demonstrate the application of financial formulas and the use of logarithms to solve for unknown variables such as time and payment amounts. The assignment also explores the comparison of different loan scenarios and the calculation of total payments and interest paid over various time periods. The problems cover a range of financial scenarios, including personal loans, mortgages, and investments, providing a comprehensive overview of financial math principles. The student has provided detailed solutions to all the questions.

Part A
Q1.
A = 3000, r = 9.5 % , n =12, PMT = 100
A= PMT * (1+ APR
n )nY
−1
( APR
n )
Taking log and solving for y we have
Y = 34 months
Q2.
P = 5500 , r = 7.2% , n = 12 , Y = 2
PMT = ( P∗r
n )/ [1−(1+ r
n )−nY
]
Monthly payment = $246.75
Q3.
A = 7500, r = 9.6 , n = 12, y = 1 , y = 5
PMT = ( P∗r
n )/ [ 1−( 1+ r
n )
−nY
]
PMT| y = 1 = $ 657.97
PMT | y = 5 = $ 157.88
Difference in the two monthly payments: (657.97 – 157.88) = $500.09

Q4.
A = 7500, r = 9.6 , n = 12, y = 2
PMT = ( P∗r
n )/ [1−(1+ r
n )−nY
]
PMT| y = 2 = $ 344.70
Total Interest paid = 344.7 *12*2 – 7500 = $772.8
Q5.
A = 1800, r = 8.4 , n = 12, y = 1 , y = 5
PMT = ( P∗r
n )/ [ 1−( 1+ r
n )
−nY
]
PMT| y = 1 = $ 156.91
PMT | y = 5 = $ 36.84
Difference in the total interest paid on the two loans : (36.84*12*5-1800)- (156.91*12-1800)
= $327.48
Q6.
R = 7.5 %, P = 18000, PMT =500 n =12,
PMT = ( P∗r
n )/ [1−(1+ r
n )−nY
]
Taking log and solving for Y

Y = 3.41 years = 41 months (approx.)
Q7.
R = 7.5 %, P = 18000, PMT =400 n =12,
PMT = ( P∗r
n )/ [1−(1+ r
n )−nY
]
Taking log and solving for Y
Y = 4.41 years = 53 months (approx.)
Total interest paid: 53* 400 – 18000 = $ 3200
Q8.
A= 17000, r = 5.5 %, n =12 , y = 5
PMT = $32.47
Q9.
A= 17000, r = 6.5 %, n =12, y = 5
Monthly payment: 33.26
A= 17000, r = 9.5 %, n =12, y = 5
Monthly payment : 35.70
Difference between the monthly payments: $2.44
Q10.

A = 10000, r = 9.9, n = 12, y = 5
PMT = ( P∗r
n )/ [1−(1+ r
n )−nY
]
Monthly payment: $211.98
Total interest paid: 211.98*12*5 – 10000 = $ 2718.8
Q11.
A= 6680, r= 6.9, PMT = 300 , n =12
PMT = ( P∗r
n )/ [ 1−( 1+ r
n )
−nY
]
Taking log on both sides to solve for y yields
Y = 2 years = 24 months
c)
Q12.
A= 14000, r = 8.75 , n =12*4*2 = 96 , y = 2
PMT = ( A∗r
n )/ [1− (1+ r
n )−nY
]
Bi weekly payment: $135.72
Q13.
PMT = $80 , r = 6% , n =12 , y = 18

PMT = ( A∗r
n )/ [1− (1+ r
n )−nY
]
Solving for A we have
A = $30,988.26
Q14.
Q15.
A = 8500+3000+12500 = $24000
N = 12
Y = 5
R = 8.9%
PMT = ( A∗r
n )/ [ 1− ( 1+ r
n )
−nY
]
Solving for PMT, we have
Monthly payment: $497.04
Total amount paid : 5*12*497.04 = $29822.4
Q16.
A= 21000, r= 8% , n = 12 , y = 3
PMT = ( A∗r
n )/ [1− (1+ r
n )−nY
]
Solving for PMT we have,

Monthly payments: $ 658.06
Total payment complete till 3 years: 658.06 *12*3 = $23690.6