Respuesta :
Answer:
$128,088.54
Step-by-step explanation:
Year Year Deposits Year Interest Total Deposits Total Interest Balance
1 $4,800.00 $72.10 $4,800.00 $72.10 $4,872.10
2 $4,800.00 $207.79 $9,600.00 $279.89 $9,879.89
3 $4,800.00 $347.25 $14,400.00 $627.15 $15,027.15
4 $4,800.00 $490.60 $19,200.00 $1,117.74 $20,317.74
5 $4,800.00 $637.94 $24,000.00 $1,755.68 $25,755.68
6 $4,800.00 $789.38 $28,800.00 $2,545.06 $31,345.06
7 $4,800.00 $945.04 $33,600.00 $3,490.11 $37,090.11
8 $4,800.00 $1,105.04 $38,400.00 $4,595.14 $42,995.14
9 $4,800.00 $1,269.49 $43,200.00 $5,864.63 $49,064.63
10 $4,800.00 $1,438.52 $48,000.00 $7,303.15 $55,303.15
11 $4,800.00 $1,612.26 $52,800.00 $8,915.41 $61,715.41
12 $4,800.00 $1,790.83 $57,600.00 $10,706.24 $68,306.24
13 $4,800.00 $1,974.38 $62,400.00 $12,680.62 $75,080.62
14 $4,800.00 $2,163.05 $67,200.00 $14,843.67 $82,043.67
15 $4,800.00 $2,356.96 $72,000.00 $17,200.63 $89,200.63
16 $4,800.00 $2,556.28 $76,800.00 $19,756.91 $96,556.91
17 $4,800.00 $2,761.14 $81,600.00 $22,518.05 $104,118.05
18 $4,800.00 $2,971.72 $86,400.00 $25,489.77 $111,889.77
19 $4,800.00 $3,188.15 $91,200.00 $28,677.92 $119,877.92
20 $4,800.00 $3,410.62 $96,000.00 $32,088.54 $128,088.54
Answer:
The account after 20 years is $73798.8.
Step-by-step explanation:
Given : James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They despoit $400. Into the account each month.
To find : How much will be in the account after 20 years ?
Solution :
Using monthly payment formula,
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor is [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Substitute in the formula,
[tex]\text{Amount}=M\times \frac{1-(1+i)^{-n}}{i}[/tex]
Where, M=$400 amount deposited monthly
r= 2.75%=0.0275 is the interest rate
[tex]i=\frac{0.0275}{12} =0.00229[/tex]
t=20 years is the time
[tex]n=12\times 20=240[/tex]
Substitute the value,
[tex]\text{Amount}=400\times \frac{1-(1+0.00229)^{-240}}{0.00229}[/tex]
[tex]\text{Amount}=400\times \frac{1-0.5775}{0.00229}[/tex]
[tex]\text{Amount}=400\times 184.497[/tex]
[tex]\text{Amount}=73798.8[/tex]
Therefore, the account after 20 years is $73798.8.
