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Homework answers / question archive / A loan of RMX is repaid with level annual payments at the end of each year for 10 years
A loan of RMX is repaid with level annual payments at the end of each year for 10 years. You are given: i) The interest paid in the first year is RM3600; and ii) The principal repaid in the 6th year is RM4871. Calculate X.
The formula for calculating the loan EMI amount is as below.
where
· A = Level payment Amount per period
· P = initial Principal (loan amount)
· r = interest rate per period
· n = total number of payments or periods
Further, Principal Repayment (PR) in any time period (i), is given by PRi = (A – r*P)*(1 + r)^(i-1)
(In the 6th period, Principal repayment was 4,871.
Interest at end of period 1, I1 = P*r or 3600 = P*r
We have two equations and two unknowns, namely P and r. We can use Excel goal seek function to find the respective variables.
Hence, The Principal X is RM 48,000
| Principal (X) | 48,000.00 | ||||
| Time Period (n) | 10 | ||||
| Interest rate (r) | 7.50% | ||||
| Period | Opening Principal | Annual Payments | Interest repayment | Principal repayment | Closing Balance |
| 1 | 48,000 | 6,993 | 3,600 | 3,393 | 44,607 |
| 2 | 44,607 | 6,993 | 3,346 | 3,647 | 40,960 |
| 3 | 40,960 | 6,993 | 3,072 | 3,921 | 37,039 |
| 4 | 37,039 | 6,993 | 2,778 | 4,215 | 32,824 |
| 5 | 32,824 | 6,993 | 2,462 | 4,531 | 28,293 |
| 6 | 28,293 | 6,993 | 2,122 | 4,871 | 23,422 |
| 7 | 23,422 | 6,993 | 1,757 | 5,236 | 18,185 |
| 8 | 18,185 | 6,993 | 1,364 | 5,629 | 12,556 |
| 9 | 12,556 | 6,993 | 942 | 6,051 | 6,505 |
| 10 | 6,505 | 6,993 | 488 | 6,505 | -0 |
| Using PMT function to calculate Annual payments | |||||
| Using IPMT function to calculate Interest payments | |||||
| Using Goal seek function and few iterations, you can calculate Principal (X) |
please see the attached file for the complete solution.
