Question
In: Accounting
QUESTION 1 How much of a yearly investment would I need to make to earn $500,000...
QUESTION 1
-
How much of a yearly investment would I need to make to earn $500,000 in 30 years at 9% interest>
A. $8,573.77
B. $617.98
C. $10,437.20
D. $3,668.18
10 points
QUESTION 2
-
If you wanted your monthly payment to be $700 per month on a loan that extends for 72 months at 8% interest, what is the amount you could borrow?
A. $59,667.19
B. $44,864.38
C. $39,924.17
D. $27,637.54
Solutions
Expert Solution
Question No.1 - Option D - $ 3,668.18
We know,
Future Value = Periodic Investment [(1+ Interest rate )Term -1] / Interest rate
Periodic Investment = ( Future Value * Interest Rate ) / [(1+ Interest rate )Term -1]
= ( $ 500,000 * 0.09 ) / [ (1+0.09)30 - 1 ]
= $ 45,000 / 12.2677
= $ 3,668.18
Question No.2 - Option C - $ 39,924.17
The solution can be derived from the table as follows:
| Month | Loan Outstanding at month beginning | Interest for the month | Repayment | Loan Outstanding at month end |
| 1 | $ 39,924.17 | $ 266.16 | $ 700.00 | $ 39,490.33 |
| 2 | $ 39,490.33 | $ 263.27 | $ 700.00 | $ 39,053.60 |
| 3 | $ 39,053.60 | $ 260.36 | $ 700.00 | $ 38,613.95 |
| 4 | $ 38,613.95 | $ 257.43 | $ 700.00 | $ 38,171.38 |
| 5 | $ 38,171.38 | $ 254.48 | $ 700.00 | $ 37,725.85 |
| 6 | $ 37,725.85 | $ 251.51 | $ 700.00 | $ 37,277.36 |
| 7 | $ 37,277.36 | $ 248.52 | $ 700.00 | $ 36,825.88 |
| 8 | $ 36,825.88 | $ 245.51 | $ 700.00 | $ 36,371.38 |
| 9 | $ 36,371.38 | $ 242.48 | $ 700.00 | $ 35,913.86 |
| 10 | $ 35,913.86 | $ 239.43 | $ 700.00 | $ 35,453.28 |
| 11 | $ 35,453.28 | $ 236.36 | $ 700.00 | $ 34,989.64 |
| 12 | $ 34,989.64 | $ 233.26 | $ 700.00 | $ 34,522.90 |
| 13 | $ 34,522.90 | $ 230.15 | $ 700.00 | $ 34,053.06 |
| 14 | $ 34,053.06 | $ 227.02 | $ 700.00 | $ 33,580.08 |
| 15 | $ 33,580.08 | $ 223.87 | $ 700.00 | $ 33,103.94 |
| 16 | $ 33,103.94 | $ 220.69 | $ 700.00 | $ 32,624.64 |
| 17 | $ 32,624.64 | $ 217.50 | $ 700.00 | $ 32,142.13 |
| 18 | $ 32,142.13 | $ 214.28 | $ 700.00 | $ 31,656.42 |
| 19 | $ 31,656.42 | $ 211.04 | $ 700.00 | $ 31,167.46 |
| 20 | $ 31,167.46 | $ 207.78 | $ 700.00 | $ 30,675.24 |
| 21 | $ 30,675.24 | $ 204.50 | $ 700.00 | $ 30,179.74 |
| 22 | $ 30,179.74 | $ 201.20 | $ 700.00 | $ 29,680.94 |
| 23 | $ 29,680.94 | $ 197.87 | $ 700.00 | $ 29,178.81 |
| 24 | $ 29,178.81 | $ 194.53 | $ 700.00 | $ 28,673.34 |
| 25 | $ 28,673.34 | $ 191.16 | $ 700.00 | $ 28,164.49 |
| 26 | $ 28,164.49 | $ 187.76 | $ 700.00 | $ 27,652.26 |
| 27 | $ 27,652.26 | $ 184.35 | $ 700.00 | $ 27,136.61 |
| 28 | $ 27,136.61 | $ 180.91 | $ 700.00 | $ 26,617.52 |
| 29 | $ 26,617.52 | $ 177.45 | $ 700.00 | $ 26,094.97 |
| 30 | $ 26,094.97 | $ 173.97 | $ 700.00 | $ 25,568.93 |
| 31 | $ 25,568.93 | $ 170.46 | $ 700.00 | $ 25,039.39 |
| 32 | $ 25,039.39 | $ 166.93 | $ 700.00 | $ 24,506.32 |
| 33 | $ 24,506.32 | $ 163.38 | $ 700.00 | $ 23,969.70 |
| 34 | $ 23,969.70 | $ 159.80 | $ 700.00 | $ 23,429.50 |
| 35 | $ 23,429.50 | $ 156.20 | $ 700.00 | $ 22,885.69 |
| 36 | $ 22,885.69 | $ 152.57 | $ 700.00 | $ 22,338.26 |
| 37 | $ 22,338.26 | $ 148.92 | $ 700.00 | $ 21,787.19 |
| 38 | $ 21,787.19 | $ 145.25 | $ 700.00 | $ 21,232.43 |
| 39 | $ 21,232.43 | $ 141.55 | $ 700.00 | $ 20,673.98 |
| 40 | $ 20,673.98 | $ 137.83 | $ 700.00 | $ 20,111.81 |
| 41 | $ 20,111.81 | $ 134.08 | $ 700.00 | $ 19,545.89 |
| 42 | $ 19,545.89 | $ 130.31 | $ 700.00 | $ 18,976.19 |
| 43 | $ 18,976.19 | $ 126.51 | $ 700.00 | $ 18,402.70 |
| 44 | $ 18,402.70 | $ 122.68 | $ 700.00 | $ 17,825.39 |
| 45 | $ 17,825.39 | $ 118.84 | $ 700.00 | $ 17,244.22 |
| 46 | $ 17,244.22 | $ 114.96 | $ 700.00 | $ 16,659.18 |
| 47 | $ 16,659.18 | $ 111.06 | $ 700.00 | $ 16,070.25 |
| 48 | $ 16,070.25 | $ 107.13 | $ 700.00 | $ 15,477.38 |
| 49 | $ 15,477.38 | $ 103.18 | $ 700.00 | $ 14,880.56 |
| 50 | $ 14,880.56 | $ 99.20 | $ 700.00 | $ 14,279.77 |
| 51 | $ 14,279.77 | $ 95.20 | $ 700.00 | $ 13,674.97 |
| 52 | $ 13,674.97 | $ 91.17 | $ 700.00 | $ 13,066.13 |
| 53 | $ 13,066.13 | $ 87.11 | $ 700.00 | $ 12,453.24 |
| 54 | $ 12,453.24 | $ 83.02 | $ 700.00 | $ 11,836.26 |
| 55 | $ 11,836.26 | $ 78.91 | $ 700.00 | $ 11,215.17 |
| 56 | $ 11,215.17 | $ 74.77 | $ 700.00 | $ 10,589.94 |
| 57 | $ 10,589.94 | $ 70.60 | $ 700.00 | $ 9,960.54 |
| 58 | $ 9,960.54 | $ 66.40 | $ 700.00 | $ 9,326.94 |
| 59 | $ 9,326.94 | $ 62.18 | $ 700.00 | $ 8,689.12 |
| 60 | $ 8,689.12 | $ 57.93 | $ 700.00 | $ 8,047.05 |
| 61 | $ 8,047.05 | $ 53.65 | $ 700.00 | $ 7,400.69 |
| 62 | $ 7,400.69 | $ 49.34 | $ 700.00 | $ 6,750.03 |
| 63 | $ 6,750.03 | $ 45.00 | $ 700.00 | $ 6,095.03 |
| 64 | $ 6,095.03 | $ 40.63 | $ 700.00 | $ 5,435.67 |
| 65 | $ 5,435.67 | $ 36.24 | $ 700.00 | $ 4,771.90 |
| 66 | $ 4,771.90 | $ 31.81 | $ 700.00 | $ 4,103.72 |
| 67 | $ 4,103.72 | $ 27.36 | $ 700.00 | $ 3,431.07 |
| 68 | $ 3,431.07 | $ 22.87 | $ 700.00 | $ 2,753.95 |
| 69 | $ 2,753.95 | $ 18.36 | $ 700.00 | $ 2,072.31 |
| 70 | $ 2,072.31 | $ 13.82 | $ 700.00 | $ 1,386.12 |
| 71 | $ 1,386.12 | $ 9.24 | $ 700.00 | $ 695.36 |
| 72 | $ 695.36 | $ 4.64 | $ 700.00 | $ - |
The table is arrived using reverse computation. Since we know that the balance at the end of 72nd month is "ZERO", we start our working there.
At the end of the month, $ 700 will be repaid after which balance comes to zero. Hence, for arriving at the opening balance, $ 700 should be discounted for 1 month using the interest rate of 8% ( monthly interest rate of 0.666666666667% ) which amounts to the $ 695.36. The opening balance of $ 695.36 together with the interest for the year of $ 4.64 will amount to $ 700.
The opening balance derived for the 72nd month is also the closing balance of the 71st month. Thus we can arrive at the amount of loan obtained.
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