Question

Question 5. (16)

1. How much do you have to deposit in your saving account if you wish to have RM40,000 in 5 years given the annual interest rate is 3% compounded monthly?                                           (2)

2. You want to take a mortgage of RM400,000 for a new house. The mortgage is financed at 6% per annum adjusted monthly over 20 years.

1. What is the monthly repayment on the mortgage?                                 (2)

2. What is the total amount paid over 20 years?                                        (2)

3. What is the total amount of interest paid over 20 years?                         (2)

4. What is the effective interest rate?                                                        (2)

5. What is the total interest paid over the 5^th year?                                     (2)

                    

6. What is the amount owing on the mortgage at the end of 5^th year?                 (2)

3. You are making monthly deposit of $2000 in your saving account. The saving rate is 3% per annum, compounded monthly. How much would the balance in your account after 2 years? (2)

Answer 1

a]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment.  

r = periodic rate of interest. This is (3%/12) = 0.25%.  We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 5 * 12 = 60 (there are 5 years, or 60 months in the investment period)

40,000 = P * [(1 + 0.25%)⁶⁰ - 1] / 0.25%

P = 40,000 * 0.25% / [(1 + 0.25%)⁶⁰ - 1]

P = 618.75

Amount to deposit in account monthly = RM 618.75

b]

(i)

Monthly loan payment is calculated using PMT function in Excel :

rate = 6% / 12   (converting annual rate into monthly rate)

nper = 20*12 (20 year loan with 12 monthly payments each year)

pv = 400000 (loan amount)

PMT is calculated to be RM 2,865.72

(ii)

Total amount paid over 20 years = monthly payment * total number of payments

Total amount paid over 20 years = RM 2,865.72 * (20 * 12)

Total amount paid over 20 years = RM 687,773.82

(iii)

Total amount of interest = total amount paid - loan amount

Total amount of interest = 687,773.82 - 400,000

Total amount of interest = RM 287,773.82

(iv)

Effective rate = (1 + (r/n))ⁿ - 1

where r = nominal rate of interest

n = number of compounding periods per year

Effective rate = (1 + (6%/12))¹² - 1

Effective rate = 6.1678%

(v)

We calculate the interest paid during 5th year using CUMIPMT function in Excel :

rate = 6% / 12   (converting annual rate into monthly rate)

nper = 20*12 (20 year loan with 12 monthly payments each year)

pv = 400000 (loan amount)

start period = 49 (We are calculating interest paid between 49th and 60th month)

end period = 60 (We are calculating interest paid between 49th and 60th month)

type = 0 (each payment is made at the end of month)

CUMIPMT is calculated to be RM 20,820.89

(vi)

We calculate the principal paid off after 5 years (60 months) using CUMPRINC function in Excel :

rate = 6% / 12   (converting annual rate into monthly rate)

nper = 20*12 (20 year loan with 12 monthly payments each year)

pv = 400000 (loan amount)

start period = 1 (We are calculating principal paid off between 1st and 60th month)

end period = 60 (We are calculating principal paid off between 1st and 60th month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be RM 60,401.61

The balance loan principal outstanding after 5 years =  400,000 - 60,401.61

The balance loan principal outstanding after 5 years = RM 339,598.39

c]

Future value of annuity = P * [(1 + r)ⁿ - 1] / r,

where P = periodic payment. This is $2,000

r = periodic rate of interest. This is (3%/12) = 0.25%.  We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 2 * 12 = 24 (there are 2 years, or 24 months in the investment period)

FV = $2,000 * [(1 + 0.25%)²⁴ - 1] / 0.25%

FV = $49,405.64