Simple Interest Calculation
1.Total amount = Principal + Interest
Principal = $ 12,500
Rate of interest = 7.5% p.a.
Time period = 18 months or 1.5 years
Simple interest = (P*R*T/100) = (12500*7.5*1.5/100) = $1,406.25
Total amount Mary repaid = 12500 + 1406.25 = $ 13,906.25
2.Principal = $4,750
Interest rate = 6% for 240 days
- Partial payment was made on March 7th to the extent of $ 650
Hence, balance loan amount = 4750 – 650 = $ 4,150
- Another partial payment to the tune of $ 1,200 was done on May 22
Hence,, balance loan amount = 4150 – 1200 = $ 2,950
- Maturity date is 240 days from January 5thwhich comes out as September 2nd.
Amount due on maturity = 2950 + (4750*6/100) = $3,235
3.
- Interest paid for the money = (3.5/100)*1800 = $63
- Money received from the bank = 1800 – 63 = $ 1,737
- Actual interest rate paid = (63/1737)*100 = 3.63%
4.Principal = $26,400
Rate of interest = 2.15% p.a. which is compounded monthly
Time period = 7 years or (12*7) = 84 months
The relevant formula is shown below.
A = P (1+ (R/n))nt
Where n highlights the number of compounding periods in an year and t is the time period in years
Amount balance after 7 years = 26400[1+ (2.15/1200)]84 = $30,683.63
5.Option 1: 2.5% compounded semi-annually
Principal = $ 10,000
One year = 2 period of 6 months
Amount due after one year = 10000*[1+ (2.5/200)]2 = $10,251.56
Option 2: 2.485% compounded weekly
Principal = $ 10,000
One year = 365/7 = 52 weeks
Amount due after one year = 10000*[1+ (2.485/5200)]52 = $10,251.55
Hence, from the above computation, it is apparent that the superior or better choice is option 1 or 2.5% interest compounded semi-annually.
6.Amount due = $45,000
Time period = 10 years or 120 months
Rate of interest = 2.25% p.a. compounded monthly
The relevant formula is shown below.
A = P (1+ (R/n))nt
Where n highlights the number of compounding periods in an year and t is the time period in years
Let the money to be invested now be X
Hence, 45000 = X[1+ (2.25/1200)]120
Solving the above, X = $35,940.8 or approximately $ 35,941
7.Using the APR table, the finance charge amounts to $11.98 per $ 100 borrowed
Total amount borrowed = (85/100)*12000 = $ 10,200
Hence, total finance charge for the above borrowing = 11.98*102 = $ 1,221.96
Total amount to be repaid = 10200 + 1221.96 = $11,421.96
Total equal monthly instalments = 36
Hence, amount of monthly payment for the loan = 11421.96/36 = $317.28
8.Total loan amount = $ 12,000
Total amount paid to discharge the above loan = 166.53*120 = $19,983.6
Hence, interest paid on the loan = 19983.6 – 12000 = $ 7.983.6
The APR computation is highlighted below.
APR = [(7983.6/12000)]/10 = 6.65%
Calculation of Loan Repayment with Interest
9.Total finance charge on the loan = (375.11*60) – 18500 = $ 4,006.6
Hence, APR = [(4006.6/18500)]/5 = 4.33%
The net present value of all payments should be equal to the loan amount i.e. $18,500. The APR would be used as the discounting factor. The requisite computation is shown below.
Total interest saved = (375.11*60) – (375.11*35) – 7043.79 = $ 2,333.96
The payoff amount for the loan = 375.11*35 + 7043.79 = $ 20,172.64
10.As per the policy, the minimum monthly payment is obtained by adding 4.35% of the outstanding principal and any new interest at the rate of 1.75% per month.
Outstanding principal as on May 1 = $ 1,854
New interest = (1.75/100)*1854*(20/30) = $ 21.63
Hence, minimum payment for the May 1 billing date = (4.35/100)*1854 + 21.63 = $ 102.28
Payment made on May 1 = $ 350
Hence, outstanding principal = 1854 – 350 + 21.63 = $ 1525.63
Interest levied for the month of May on the above unpaid balance = (1.75/100)*1525.63 = $26.70
Total balance due on June 1 = 1525.63 +26.70 = $1,552.33
11.As per the previous balance method, interest is levied on the amount outstanding at the end of the previous month irrespective of the transactions that have taken place in the current month.
Outstanding balance as on October 3 = $854.72
Applicable interest rate = 1.8% per month
Hence, finance charge on November 3 = (1.8/100)*854.72 = $ 15.38
12.The balances for the month of September based on the given information are computed below.
September 1 to September 4 = $ 934.10
September 5 to September 12 = 934.10 -175 = $ 759.1
September 13 to September 21 = 759.1 + 49.14 = $ 808.24
September 22 to September 28 = 808.24 + 80.66 = $ 888.90
September 29 to September 30 = 888.90 + 112.46 = $ 1001.36
Hence, average daily balance for month of September = [(934.1*4) +(759.1*8) + (808.24*9) + (888.90*7) + (1001.36*2)]/30 = $ 843.61
Thus, finance charge on October 1 = (1.3/100)*843.61 = $ 10.97
13.Consider the total gross income earned by Yee in 52 months = 7245*52 = $ 376,740
Total repayments for the car loan = 345*15 = $ 5,175
Total repayments for the television = 125*7 = $ 875
Total repayments for the student loan = 245*52 = $ 12740
Hence, adjusted income over 52 months = 376740 – 5175 – 875 – 12740 = $ 357,950
Therefore, monthly adjusted income = (357950/52) = $ 6,883.65
Maximum monthly payment for the home loan = 0.28*6883.65 = $ 1,927.4
14.Price of condominium = $ 295,000
Down payment required = 0.2*295,000 = $ 59,000
Hence, principal amount for the mortgage = 295000 – 59000 = $ 236,000
Principal amount = $ 236,000
Time period = 15 years or 180 months
Rate of interest = 5% per annum or (5/12 = 0.4167%) per month
The relevant formula for equal monthly instalment determination is given below.
EMI = [P x R x (1+R)N]/[(1+R)N -1]
Thus, EMI = 236000*0.004167*(1.004167)180/(1.004167180-1) = $ 1866. 27
Principal amount = $ 236,000
Time period = 30 years or 360 months
Rate of interest = 5.5% per annum or (5.5/12 = 0.4583%) per month
The relevant formula for equal monthly instalment determination is given below.
EMI = [P x R x (1+R)N]/[(1+R)N -1]
Thus, EMI = 236000*0.004583*(1.004583)360/(1.004583360-1) = $ 1,339.98
15.Price of house = $ 305,000
Mortgage principal = (0.8*305000) = $ 244,000
Time period for loan repayment = 30 years or 360 months
Rate of interest = 4.5% p.a. or (4.5/12 = 0.375%) per month
The relevant formula for equal monthly instalment determination is given below.
EMI = [P x R x (1+R)N]/[(1+R)N -1]
Thus, EMI = 244000*0.00375*(1.00375)360/(1.00375360-1) = $ 1,236.31
However, besides the EMI for the mortgage, there are certain additional payments highlighted below.
Monthly association due = $ 125
Monthly home insurance expense = (2000/12) = $ 166.67
Monthly tax payment = (3149/12) = $ 262.42
Hence, total monthly amount that Harrison will pay for the house = 1,236.31 + 125 + 166.67 + 262.42 = $ 1,790.4
16.Total principal for the car loan = $ 26,450
Loan duration = 4 years or 48 months
Rate of interest = 2.5% p.a. or (2.5/12 = 0.2083%) per month
The relevant formula for equal monthly instalment determination is given below.
EMI = [P x R x (1+R)N]/[(1+R)N -1]
Thus, EMI = 26450*0.002083*1.00208348/(1.00208348 – 1) = $ 579.63
Total amount paid to discharge the loan over 4 years = 579.63 *48 = $27,822.06
However, the principal to be repaid was $ 26,450. Hence, any incremental payment would be on account of interest payment.
Thus, total interest paid = $27,822.06 – $ 26,450 = $ 1,372.06
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