Question

In: Finance

Sarah secured a bank loan of $155,000 for the purchase of a house. The mortgage is...

Sarah secured a bank loan of $155,000 for the purchase of a house. The mortgage is to be amortized through monthly payments for a term of 15 years, with an interest rate of 3%/year compounded monthly on the unpaid balance. She plans to sell her house in 5 years. How much will Sarah still owe on her house? (Round your answer to the nearest cent.)

Solutions

Expert Solution

EMI :

EMI = Loan / PVAF (r%, n)
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

Particulars Amount
Loan Amount $         1,55,000.00
Int rate per Month 0.2500%
No. of Months 180

EMI = Loan Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 155000 / PVAF (0.0025 , 180)
= $ 155000 / 144.8055
= $ 1070.4

Particulars Amount
Loan Amount $ 1,55,000.00
Int rate per Month 0.2500%
No. of Months 180
Outstanding Bal after 60
EMI $      1,070.40
Payments Left 120

Outstanding Bal = Instalment * [ 1 - ( 1 + r )^ - n ] / r
= $ 1070.4 * [ 1 - ( 1 + 0.0025 ) ^ - 120 ] / 0.0025
= $ 1070.4 * [ 1 - ( 1.0025 ) ^ - 120 ] / 0.0025
= $ 1070.4 * [ 1 - 0.741096 ] / 0.0025
= $ 1070.4 * [ 0.258904 ] / 0.0025
= $ 110852.34

r = Int Rate per period
n = Balance No. of periods
Amount still owede after 5 Years is $ 110852.34

Amortization Table:

Period Opening Bal EMI Int Principal Repay Closing Outstanding
1 $         1,55,000.00 $         1,070.40 $               387.50 $                682.90 $            1,54,317.10
2 $         1,54,317.10 $         1,070.40 $               385.79 $                684.61 $            1,53,632.49
3 $         1,53,632.49 $         1,070.40 $               384.08 $                686.32 $            1,52,946.17
4 $         1,52,946.17 $         1,070.40 $               382.37 $                688.04 $            1,52,258.13
5 $         1,52,258.13 $         1,070.40 $               380.65 $                689.76 $            1,51,568.38
6 $         1,51,568.38 $         1,070.40 $               378.92 $                691.48 $            1,50,876.90
7 $         1,50,876.90 $         1,070.40 $               377.19 $                693.21 $            1,50,183.69
53 $         1,17,128.02 $         1,070.40 $               292.82 $                777.58 $            1,16,350.43
54 $         1,16,350.43 $         1,070.40 $               290.88 $                779.53 $            1,15,570.91
55 $         1,15,570.91 $         1,070.40 $               288.93 $                781.47 $            1,14,789.43
56 $         1,14,789.43 $         1,070.40 $               286.97 $                783.43 $            1,14,006.01
57 $         1,14,006.01 $         1,070.40 $               285.02 $                785.39 $            1,13,220.62
58 $         1,13,220.62 $         1,070.40 $               283.05 $                787.35 $            1,12,433.27
59 $         1,12,433.27 $         1,070.40 $               281.08 $                789.32 $            1,11,643.95
60 $         1,11,643.95 $         1,070.40 $               279.11 $                791.29 $           1,10,852.66
61 $         1,10,852.66 $         1,070.40 $               277.13 $                793.27 $            1,10,059.39
62 $         1,10,059.39 $         1,070.40 $               275.15 $                795.25 $            1,09,264.14

Pls do rate, if the answer is correct and comment, if any further assistance is required.


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