Question

show work please

Borrowing $10 Per Month We continue with the same example: you borrow $10 per month from your friend. On each of these loans, your friend charges 30% Amount loan atthe year S10 Number ofowed on Loan amount Month months of interest end of thein interest per year, compounded monthly Determining the total amount that you owe at the end of one year will require a few steps $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 $10 12 We first have to calculate the interest on the individual $10 loans separately. (It will be easier to calculate the amount owed for the LAST $10 first and work backwards.) 10 For convenience, assume that you borrow the new $10 on the same day of the month that interest is added to the balance for the older $10 loans. This means that no interest is charged for the last $10 loan, one month of interest is charged for the second-to-last $10 loan, and so on. Use the compound interest formula to complete the table Look for a pattern the numbers in the last column. In full sentences below, describe what you do to the number in one row to get to the number in the next row

Answer 1

Solution: Let Principal be $R, Rate =R% p.a, Time =t years.

(i) When interest is compounded annually:

Amount after t years

= P(1 + 100

(ii) When interest is compounded half-yearly:

Principal = $R, Rate =R% p.a=(R/2)% per half-yearly,Time =t years=(2t) half-years

Amount after t years

R/2 100

(iii) When interest is compounded quarterly:

Principal = $R, Rate =R% p.a=(R/4)% per quarter,Time = t years=(4t) quarters.

Amount after t years

At R/4 100

(iv) When interest is compounded monthly:

Principal = $R, Rate =R% p.a=(R/12)% per month,Time = t years=(12t) months.

Amount after t years

12t 100

In our problem, I borrow $10 per month from my friend. On each of these loans, my friend charges 30% in interest per year, compounded monthly.

For 12th month loan amount = $10.

Number of months of interest =0

Therefore, amount owed on loan at the end of the year =$10(No interest)

For 11th month loan amount = $10.

Number of months of interest =1

Therefore, amount owed on loan at the end of the year

R/12 100

0110) 30/12

-106-ל

For 10th month loan amount = $10.

Number of months of interest =2

Therefore, amount owed on loan at the end of the year

R/12 100

30/12 10 1 + 100

$=10\left ( 1+\frac{1}{40} \right )^{2}$

$=10*1.0506=10.506$

For 9th month loan amount = $10.

Number of months of interest =3

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{3}$

For 8th month loan amount = $10.

Number of months of interest =4

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{4}$

$=10*1.1038=11.038$

For 7th month loan amount = $10.

Number of months of interest =5

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{5}$

$=10*1.1314=11.314$

For 6th month loan amount = $10.

Number of months of interest =6

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{6}$

$=10*1.1596=11.596$

For 5th month loan amount = $10.

Number of months of interest =7

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{7}$

$=10*1.1886\right )=11.886$

For 4th month loan amount = $10.

Number of months of interest =8

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{8}$

$=10*1.2180\right )=12.18$

For 3rd month loan amount = $10.

Number of months of interest =9

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{9}$

$=10*1.2488\right )=12.488$

For 2nd month loan amount = $10.

Number of months of interest =10

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{10}$

$=10*1.2800\right )=12.8$

For 1st month loan amount = $10.

Number of months of interest =11

Therefore, amount owed on loan at the end of the year

$=10\left ( 1+\frac{1}{40} \right )^{11}$

$=10*1.3120\right )=13.12$

Therefore,

Month	Loan amount	Number of months of interest	Amount owed on loan at the end of the year
12	$10	0	$10
11	$10	1	10.25
10	$10	2	10.50
9	$10	3	10.768
8	$10	4	11.038
7	$10	5	11.314
6	$10	6	11.596
5	$10	7	11.886
4	$10	8	12.18
3	$10	9	12.488
2	$10	10	12.8
1	$10	11	13.12