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(Annuity payments) Mr. Bill S.​ Preston, Esq., purchased a new house for ​$100,000. He paid ​$15,000...

(Annuity payments) Mr. Bill S.​ Preston, Esq., purchased a new house for ​$100,000. He paid ​$15,000 upfront and agreed to pay the rest over the next 25 years in 25 equal annual payments that include principal payments plus 8 percent compound interest on the unpaid balance.

What will these equal payments​ be?

Mr. Bill S.​ Preston, Esq., purchased a new house for ​$100,000 and paid $15,000 upfront. How much does he need to borrow to purchase the​ house?

Solutions

Expert Solution

Amount borrowed = price of house-upfront payment = 100000-15000=85000

Annual rate(M)= yearly rate/12= 8.00% Annual payment= 7962.70
Year Beginning balance (A) Annual payment Interest = M*A Principal paid Ending balance
1 85000.00 7962.70 6800.00 1162.70 83837.30
2 83837.30 7962.70 6706.98 1255.71 82581.59
3 82581.59 7962.70 6606.53 1356.17 81225.42
4 81225.42 7962.70 6498.03 1464.66 79760.76
5 79760.76 7962.70 6380.86 1581.84 78178.93
6 78178.93 7962.70 6254.31 1708.38 76470.54
7 76470.54 7962.70 6117.64 1845.05 74625.49
8 74625.49 7962.70 5970.04 1992.66 72632.83
9 72632.83 7962.70 5810.63 2152.07 70480.76
10 70480.76 7962.70 5638.46 2324.24 68156.53
11 68156.53 7962.70 5452.52 2510.17 65646.35
12 65646.35 7962.70 5251.71 2710.99 62935.37
13 62935.37 7962.70 5034.83 2927.87 60007.50
14 60007.50 7962.70 4800.60 3162.10 56845.40
15 56845.40 7962.70 4547.63 3415.06 53430.34
16 53430.34 7962.70 4274.43 3688.27 49742.07
17 49742.07 7962.70 3979.37 3983.33 45758.74
18 45758.74 7962.70 3660.70 4302.00 41456.74
19 41456.74 7962.70 3316.54 4646.16 36810.59
20 36810.59 7962.70 2944.85 5017.85 31792.74
21 31792.74 7962.70 2543.42 5419.28 26373.46
22 26373.46 7962.70 2109.88 5852.82 20520.64
23 20520.64 7962.70 1641.65 6321.04 14199.60
24 14199.60 7962.70 1135.97 6826.73 7372.87
25 7372.87 7962.70 589.83 7372.87 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

jeff jeffy answered 2 years ago
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