Question

Oliver borrows $300,000 from a bank and agrees to repay the bank with equal payments at the end of each year for 30 years based on an annual effective interest rate of 5%.

After making the 10^th payment, the bank allows Oliver to make no payments for 10 years, with increased level payments after that.

At the end of the 30-year period, the loan is fully paid.

How much does Oliver pay each year when he resumes payment? Possible answers are 39,000 or 51,300 or 52,500 or 55,700 or 58,500

Answer 1

Particulars	Amount
Loan Amount	$         3,00,000.00
Int rate per Anum	5.0000%
No. of Years	30

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 300000 / PVAF (0.05 , 30)
= $ 300000 / 15.3725
= $ 19515.43

PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

How to calculate PVAF using Excel:
=PV(Rate,NPER,-1)
Rate = Disc Rate
NPER = No.of periods
Loan AMortization Schedle for 10 Years:

Period	Opening Bal	EMI	Int	Principal Repay	Closing Outstanding
1	$         3,00,000.00	$       19,515.43	$          15,000.00	$            4,515.43	$            2,95,484.57
2	$         2,95,484.57	$       19,515.43	$          14,774.23	$            4,741.20	$            2,90,743.37
3	$         2,90,743.37	$       19,515.43	$          14,537.17	$            4,978.26	$            2,85,765.11
4	$         2,85,765.11	$       19,515.43	$          14,288.26	$            5,227.18	$            2,80,537.93
5	$         2,80,537.93	$       19,515.43	$          14,026.90	$            5,488.53	$            2,75,049.40
6	$         2,75,049.40	$       19,515.43	$          13,752.47	$            5,762.96	$            2,69,286.44
7	$         2,69,286.44	$       19,515.43	$          13,464.32	$            6,051.11	$            2,63,235.33
8	$         2,63,235.33	$       19,515.43	$          13,161.77	$            6,353.66	$            2,56,881.66
9	$         2,56,881.66	$       19,515.43	$          12,844.08	$            6,671.35	$            2,50,210.31
10	$         2,50,210.31	$       19,515.43	$          12,510.52	$            7,004.91	$            2,43,205.40

As there is No payment for 10 Years, FV at 20 Years ( 10 Years Gap ).:

Future Value:
FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$      2,43,205.40
Int Rate	5.0000%
Periods	10

Future Value = Present Value * ( 1 + r )^n
= $ 243205.4 ( 1 + 0.05) ^ 10
= $ 243205.4 ( 1.05 ^ 10)
= $ 243205.4 * 1.6289
= $ 396155.97
Recomputation of Annual Instalment for balance 10 Years:

Particulars	Amount
Loan Amount	$         3,96,155.97
Int rate per Anum	5.0000%
No. of Years	10

Annual Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per Anum & n is No. of Years
= $ 396155.97 / PVAF (0.05 , 10)
= $ 396155.97 / 7.7217
= $ 51304.01
Answer $ 51300 is correct. Difference is Rounding off diff.