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1 Bank Muscat offering 2
1 Bank Muscat offering 2.8 percent compounded daily on its savings accounts. If you deposit 2,000 OMR today, how much will you have in the account in 10 years?
2
hmad’s widow receives $100000. She intend to receive monthly salary. The insurance company is welling to pay her $2500 monthly.The interest rate is J12=6%. What is the concluding payment a. $1,482.46 b. $2,4182.46 c. $1,842.46 d. $4,182.46
Expert Solution
1 principal amount = 2000
rate of interest ( assumed to be per annum) = 2.8%p.a. compounded daily.
so here n = 365 days
t = 10 years
and i = 2.8% & i/n = 2.8%/365 = 0.007671%
so , amount after 10 years will be = p(1+i/n)^nt = 2000(1 + 0.007671%)^3650
= 2646.23 OMR
and compound interest earned during 10 years , compounded annually = 2646.23-2000 = 646.23 omr
2
Principal = $100,000
Annuity = $2500 (monthly)
Interest rate = 6%
Monthly interest rate = 6%/12= 0.5%
Using the loan amortization formula
Annuity = Principal *( Monthly interest rate / (1- (1 + Monthly interest rate)-no of periods)
$2,500 = $100,000 * (0.5% / (1 - (1+0.5%)-no of periods)
Solving for no of periods using Texas Instruments BA II plus calculator
Set PMT = 2500, PV= -100,000, I/Y=0.5%, FV=0 CPT--> N
We gat no of periods = 44.74
So the last payment must be made in the 45th period
Using the amortization table to solve for the last value
Interest = Monthly interest rate * Beginning Balance
Interest = 0.5% * $100,000
Interest = $500
Accumulated Amount = Beginning balance + Interest
Accumulated Amount = $100,000 + $500
Accumulated Amount = $100,500
Ending balance = Accumulated Amount - Monthly payment
Ending balance = $100,500 - $2,500
Ending balance = $98,000
| Month | Beginning Balance | Interest | Accumulated Amount | Monthly payment | Ending balance |
| 1 | $100,000.00 | $500.00 | $100,500.00 | $2,500.00 | $98,000.00 |
| 2 | $98,000.00 | $490.00 | $98,490.00 | $2,500.00 | $95,990.00 |
| 3 | $95,990.00 | $479.95 | $96,469.95 | $2,500.00 | $93,969.95 |
| 4 | $93,969.95 | $469.85 | $94,439.80 | $2,500.00 | $91,939.80 |
| 5 | $91,939.80 | $459.70 | $92,399.50 | $2,500.00 | $89,899.50 |
| 6 | $89,899.50 | $449.50 | $90,349.00 | $2,500.00 | $87,849.00 |
| 7 | $87,849.00 | $439.24 | $88,288.24 | $2,500.00 | $85,788.24 |
| 8 | $85,788.24 | $428.94 | $86,217.18 | $2,500.00 | $83,717.18 |
| 9 | $83,717.18 | $418.59 | $84,135.77 | $2,500.00 | $81,635.77 |
| 10 | $81,635.77 | $408.18 | $82,043.95 | $2,500.00 | $79,543.95 |
| 11 | $79,543.95 | $397.72 | $79,941.67 | $2,500.00 | $77,441.67 |
| 12 | $77,441.67 | $387.21 | $77,828.88 | $2,500.00 | $75,328.88 |
| 13 | $75,328.88 | $376.64 | $75,705.52 | $2,500.00 | $73,205.52 |
| 14 | $73,205.52 | $366.03 | $73,571.55 | $2,500.00 | $71,071.55 |
| 15 | $71,071.55 | $355.36 | $71,426.90 | $2,500.00 | $68,926.90 |
| 16 | $68,926.90 | $344.63 | $69,271.54 | $2,500.00 | $66,771.54 |
| 17 | $66,771.54 | $333.86 | $67,105.40 | $2,500.00 | $64,605.40 |
| 18 | $64,605.40 | $323.03 | $64,928.42 | $2,500.00 | $62,428.42 |
| 19 | $62,428.42 | $312.14 | $62,740.57 | $2,500.00 | $60,240.57 |
| 20 | $60,240.57 | $301.20 | $60,541.77 | $2,500.00 | $58,041.77 |
| 21 | $58,041.77 | $290.21 | $58,331.98 | $2,500.00 | $55,831.98 |
| 22 | $55,831.98 | $279.16 | $56,111.14 | $2,500.00 | $53,611.14 |
| 23 | $53,611.14 | $268.06 | $53,879.19 | $2,500.00 | $51,379.19 |
| 24 | $51,379.19 | $256.90 | $51,636.09 | $2,500.00 | $49,136.09 |
| 25 | $49,136.09 | $245.68 | $49,381.77 | $2,500.00 | $46,881.77 |
| 26 | $46,881.77 | $234.41 | $47,116.18 | $2,500.00 | $44,616.18 |
| 27 | $44,616.18 | $223.08 | $44,839.26 | $2,500.00 | $42,339.26 |
| 28 | $42,339.26 | $211.70 | $42,550.96 | $2,500.00 | $40,050.96 |
| 29 | $40,050.96 | $200.25 | $40,251.21 | $2,500.00 | $37,751.21 |
| 30 | $37,751.21 | $188.76 | $37,939.97 | $2,500.00 | $35,439.97 |
| 31 | $35,439.97 | $177.20 | $35,617.17 | $2,500.00 | $33,117.17 |
| 32 | $33,117.17 | $165.59 | $33,282.75 | $2,500.00 | $30,782.75 |
| 33 | $30,782.75 | $153.91 | $30,936.67 | $2,500.00 | $28,436.67 |
| 34 | $28,436.67 | $142.18 | $28,578.85 | $2,500.00 | $26,078.85 |
| 35 | $26,078.85 | $130.39 | $26,209.24 | $2,500.00 | $23,709.24 |
| 36 | $23,709.24 | $118.55 | $23,827.79 | $2,500.00 | $21,327.79 |
| 37 | $21,327.79 | $106.64 | $21,434.43 | $2,500.00 | $18,934.43 |
| 38 | $18,934.43 | $94.67 | $19,029.10 | $2,500.00 | $16,529.10 |
| 39 | $16,529.10 | $82.65 | $16,611.75 | $2,500.00 | $14,111.75 |
| 40 | $14,111.75 | $70.56 | $14,182.31 | $2,500.00 | $11,682.31 |
| 41 | $11,682.31 | $58.41 | $11,740.72 | $2,500.00 | $9,240.72 |
| 42 | $9,240.72 | $46.20 | $9,286.92 | $2,500.00 | $6,786.92 |
| 43 | $6,786.92 | $33.93 | $6,820.86 | $2,500.00 | $4,320.86 |
| 44 | $4,320.86 | $21.60 | $4,342.46 | $2,500.00 | $1,842.46 |
| 45 | $1,842.46 | $9.21 | $1,851.67 | $2,500.00 | -$648.33 |
If we see the amortization table we find the last payment would be $1842.46 because after that $2,500 monthly payment cannot be made
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