Question

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. How much will be in the account after 20 years.

Answer 1

$128,088.54

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 2

The account after 20 years is $73798.8.

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,

`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor is
`D=(1-(1+i)^(-n))/(i)`

Substitute in the formula,

`\text{Amount}=M* (1-(1+i)^(-n))/(i)`

Where, M=$400 amount deposited monthly

r= 2.75%=0.0275 is the interest rate

`i=(0.0275)/(12) =0.00229`

t=20 years is the time

`n=12* 20=240`

Substitute the value,

`\text{Amount}=400* (1-(1+0.00229)^(-240))/(0.00229)`

`\text{Amount}=400* (1-0.5775)/(0.00229)`

`\text{Amount}=400* 184.497`

`\text{Amount}=73798.8`

Therefore, the account after 20 years is $73798.8.