Question

--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?

Answer 1

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.