In: Finance
(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?
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 |