Question

Rino just purchased his first car with a 7.5% 5 year mortgage loan of RM78,000. (a) If he pays interest yearly and the total loan will be settled at the end of year 5, how much is his equal yearly payment for the sinking fund which earns 5.2% interest yearly compounding? Assume that the first payment to the fund make immediately. (b) Refer to part (a), if Rino did not pay interest to the lender for the whole tenure till end of year 5 and the first payment make to the sinking fund is one year from now, find the equal yearly payment to the fund. Ans: (a) RM 13,364.78 (b) RM 20,184.59

Answer 1

(a) Rate of interest for mortgage loan = 7.5%, Period of loan = 5 years, Mortgage loan = RM78000

Since Rino pays interest yearly and total loan will be settled at end of the year 5, therefore amount due at the end of 5 years will be be equal to mortgage loan i.e. RM78000

Rate of interest for sinking fund = 5.2% per year compounded annually

To find the equal yearly payment to sinking fund we will use pmt function in excel

Formula to be used in excel: =pmt(rate,nper,pv,-fv,type)

In the formula we will take type=1 as equal payments to sinking fund are made at the beginning of the year and pv=0 because there is no initial lumpsum deposit to the sinking fund

Using pmt function in excel we get yearly payment to sinking fund = 13364.78

(b). Since Rino did not pay any interest for the whole tenure of the loan

Hence amount due at end of 5 years = Mortgage loan x ( 1 + Rate of interest for mortgage loan)^{no of years}

= 78000 x (1 + 7.5%)⁵ = 78000 x 1.075⁵ = 78000 x 1.435629326 = 111979.0874 = 111979.08

To find the equal yearly payment to sinking fund we will use pmt function in excel

Formula to be used in excel: =pmt(rate,nper,pv,-fv,type)

In the formula we will take type=0 as equal payment to sinking fund are made at the end of the year and pv=0 because there is no initial lumpsum deposit to the sinking fund

Using pmt function in excel we get yearly payment = 20184.59