Question

# A loan of 50,000 euros is to be repaid in equal quarterly installments in five years....

A loan of 50,000 euros is to be repaid in equal quarterly installments in five years. If the annual interest rate is 7.5%, find out
a) the amount of the installment,
b) the total amount of the interest paid,
c) interest paid quarterly,
d) the first year of installments.

Part A:

Equal Quarter Instalment = Loan / PVAF (r%, n)

r = Int rate per quarter

n is no. of quarters

 Particulars Amount Loan Amount €   50,000.00 Int Rate per Quarter 1.8750% No. of periods 20 EQI = Loan Amount / PVAF (r%, n) Where r is Int rate per Quarter & n is no. of Quarters = Euro 50,000 / PVAF (0.01875 , 20) = Euro 50,000 / 16.5504 = Euro 3021.08

Part B:

Total Int Paid = [ EQI * Instalments ] - Loan

= [ Euro 3021.08 * 20 ] - Euro 50,000

= Euro 60,421.60 - Euro 50,000

= Euro 10,421.60

Part C:

 Period Opening Bal EMI Int Principal Repay Closing Outstanding 1 50,000.00 3,021.08 937.50 2,083.58 47,916.42 2 47,916.42 3,021.08 898.43 2,122.64 45,793.78 3 45,793.78 3,021.08 858.63 2,162.44 43,631.34 4 43,631.34 3,021.08 818.09 2,202.99 41,428.35 5 41,428.35 3,021.08 776.78 2,244.29 39,184.06 6 39,184.06 3,021.08 734.70 2,286.37 36,897.69 7 36,897.69 3,021.08 691.83 2,329.24 34,568.44 8 34,568.44 3,021.08 648.16 2,372.92 32,195.53 9 32,195.53 3,021.08 603.67 2,417.41 29,778.12 10 29,778.12 3,021.08 558.34 2,462.74 27,315.38 11 27,315.38 3,021.08 512.16 2,508.91 24,806.47 12 24,806.47 3,021.08 465.12 2,555.95 22,250.52 13 22,250.52 3,021.08 417.20 2,603.88 19,646.64 14 19,646.64 3,021.08 368.37 2,652.70 16,993.94 15 16,993.94 3,021.08 318.64 2,702.44 14,291.50 16 14,291.50 3,021.08 267.97 2,753.11 11,538.39 17 11,538.39 3,021.08 216.34 2,804.73 8,733.66 18 8,733.66 3,021.08 163.76 2,857.32 5,876.34 19 5,876.34 3,021.08 110.18 2,910.89 2,965.45 20 2,965.45 3,021.08 55.63 2,965.45 0.00

Part D:

Period Opening Bal EMI Int Principal Repay Closing Outstanding
1        50,000.00 3,021.08              937.50             2,083.58                   47,916.42
2        47,916.42 3,021.08              898.43             2,122.64                   45,793.78
3        45,793.78 3,021.08              858.63             2,162.44                   43,631.34
4        43,631.34 3,021.08              818.09             2,202.99                   41,428.35
5        41,428.35 3,021.08              776.78             2,244.29                   39,184.06
6        39,184.06 3,021.08              734.70             2,286.37                   36,897.69
7        36,897.69 3,021.08              691.83             2,329.24                   34,568.44
8        34,568.44 3,021.08              648.16             2,372.92                   32,195.53
9        32,195.53 3,021.08              603.67             2,417.41                   29,778.12
10        29,778.12 3,021.08              558.34             2,462.74                   27,315.38
11        27,315.38 3,021.08              512.16             2,508.91                   24,806.47
12        24,806.47 3,021.08              465.12             2,555.95                   22,250.52
13        22,250.52 3,021.08              417.20             2,603.88                   19,646.64
14        19,646.64 3,021.08              368.37             2,652.70                   16,993.94
15        16,993.94 3,021.08              318.64

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