A mobile home worth $56,000 is purchased with a down payment of $6,000 and monthly month-end...

A mobile home worth $56,000 is purchased with a down payment of $6,000 and monthly month-end payments for 15 years. If the interest rate is 9% per annum compounded monthly, determine the balance just after the 10^th payment, in 2 decimal places.

Expert Solution

Mobile home worth = $ 56000

Down payment = $ 6000

Balance Due amount = $ 56000 - $ 6000 = $ 50000

Interest rate per year = 9 %

interest rate per month = 9 % / 12 = 0.75 % or 0.0075

No. of months = 15 years * 12 = 180 months

Particulars	Amount
Balance Due Amount	$ 50,000.00
Int rate per Month	0.7500%
No. of Months	180

Equal monthly payment = Balance Due Amount / PVAF (r%, n)
Where r is Int rate per Month & n is No. of Months
= $ 50000 / PVAF (0.0075 , 180)
= $ 50000 / 98.5934
= $ 507.13
Equal monthly payment = $ 507.13

PV Annuity Factor = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.0075)^-180]] /0.0075
= [ 1 - [(1.0075)^-180]] /0.0075
= [ 1 - [0.26055]] /0.0075
= [0.73945]] /0.0075
= 98.5934

Period	Opening Bal	Monthly payment	Int	Principal Repay	Closing Outstanding
1	$ 50,000.00	$ 507.13	$ 375.00	$ 132.13	$ 49,867.87
2	$ 49,867.87	$ 507.13	$ 374.01	$ 133.12	$ 49,734.74
3	$ 49,734.74	$ 507.13	$ 373.01	$ 134.12	$ 49,600.62
4	$ 49,600.62	$ 507.13	$ 372.00	$ 135.13	$ 49,465.49
5	$ 49,465.49	$ 507.13	$ 370.99	$ 136.14	$ 49,329.35
6	$ 49,329.35	$ 507.13	$ 369.97	$ 137.16	$ 49,192.19
7	$ 49,192.19	$ 507.13	$ 368.94	$ 138.19	$ 49,053.99
8	$ 49,053.99	$ 507.13	$ 367.90	$ 139.23	$ 48,914.77
9	$ 48,914.77	$ 507.13	$ 366.86	$ 140.27	$ 48,774.49
10	$ 48,774.49	$ 507.13	$ 365.81	$ 141.32	$ 48,633.17
11	$ 48,633.17	$ 507.13	$ 364.75	$ 142.38	$ 48,490.78
12	$ 48,490.78	$ 507.13	$ 363.68	$ 143.45	$ 48,347.33

Balance after 10^th Payment = $ 48,633.17

Please comment if any further explanation is required.

jeff jeffy answered 2 years ago

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