--There is a layer of ice four inches thick covering a small pond when the weather arrives and it begins to smelt. It smelts 1/16 inch the first day, 1/8 inch the second day. 1/4 inch the third day, and keeps doubling the amount melted each succeeding day. all the ice will be melted on day number______?
--A TV set can be bought for $500 cash or by 5 monthly payments of $100 along with and interest charge. An interest charge of 1% of the unpaid balance is assessed every month, starting with $500 as the unpaid balance for the first month. How much more is paid for the TV set using the monthly payments than paying cash?
1. 1/16 = 2^0/16 = 2^(d-1)/16.
2. 2/16 = 2^1/16 = 2^(d-1)/16.
3. 4/16 = 2^2/16 = 2^(d-1)/16.
d. 64/16= 2^6/16 = 2^(d-1)/16.
2^(d-1)/16 = 64/16.
2^(d-1)/16 = 2^6/16
Multiply both sides by 16:
2^(d-1) = 2^6
d-1 = 6
d = 7th day.
2. Loan Amount: $500.
Payments.
Prin. Int.--Bal.
$100--$5.---$400.
$100--$4.---$300.
$100--$3.---$200.
$100--$2.---$100.
$100--$1.---$000.
Total Int. = $15.
Total Amt. Pd = $500 + $15 = $515.
$515 - $500 = $15. More than the cash deal.
To solve the first question, we need to find the total number of days it takes for the ice to completely melt.
On the first day, the ice melts 1/16 inch.
On the second day, it melts 1/8 inch.
On the third day, it melts 1/4 inch.
We can observe a pattern here: The amount melted is doubling each day. This means that on the next day, it will melt twice the amount of the previous day.
By writing out the sequence of the amounts melted, we can find the total number of days it takes for the ice to completely melt.
Day 1: 1/16 inch
Day 2: 1/8 inch
Day 3: 1/4 inch
Day 4: 1/2 inch
Day 5: 1 inch
Day 6: 2 inches
Day 7: 4 inches
As we can see, on the seventh day, the ice completely melts. Therefore, the ice will be melted on day number 7.
Now, let's move on to the second question.
To calculate the total amount paid when making monthly payments for the TV set, we need to find out how many months it would take to pay off the balance.
The TV set costs $500, and the monthly payment is $100 with a 1% interest charge assessed every month.
In the first month, the unpaid balance is $500.
In the second month, the unpaid balance is reduced by the monthly payment, which is $500 - $100 = $400. An interest charge of 1% is assessed on this unpaid balance.
In the third month, the unpaid balance is further reduced by the monthly payment, which is $400 - $100 = $300. Again, an interest charge of 1% is assessed on this unpaid balance.
This pattern continues until the unpaid balance reaches zero. Let's calculate the number of months required to pay off the balance.
Month 1: $500 unpaid balance
Month 2: $400 unpaid balance (after 1% interest charge)
Month 3: $300 unpaid balance (after 1% interest charge)
Month 4: $200 unpaid balance (after 1% interest charge)
Month 5: $100 unpaid balance (after 1% interest charge)
Month 6: $0 unpaid balance (after 1% interest charge)
Therefore, it takes 6 months to pay off the balance.
Now, let's calculate how much more is paid for the TV set using monthly payments compared to paying cash.
Using the monthly payments, a total of 6 payments of $100 each are made. This amounts to 6 * $100 = $600.
The cash price for the TV set is $500.
To calculate the difference, we subtract the cash price from the total amount paid using monthly payments: $600 - $500 = $100.
Therefore, $100 more is paid for the TV set using the monthly payments compared to paying cash.