Question

Help me, please!!

If you had a nickel (.05 or five cents) that earned 100 percent interest each day or doubled in value each day. How much would you have after 10 days?

Answer 1

Having a nickel doubled for 10 days gives 512 nickels, or 2560 cents.

Explanation:

Having a nickel doubled in value each day for 10 days, we first write the amount of nickels we have in the first few days, inspect what pattern these numbers take, write a general formula for the sequence formed, and use the formula to find the 10th number easily.

For the first five days we have:

Day1: 1

Day2: 1 + 1 = 2

Day 3: 2 + 2 = 4

Day 4: 4 + 4 = 8

Day 5: = 8 + 8 = 16

...

This is a geometric progression, where the first term is 1, and the common ratio is 2.

The nth term is given as

Tn = ar^(n - 1)

Tn = 1 × 2^(n - 1)

= 2^(n - 1)

That is

Day n = 2^(n - 1)

Day 10 = 2^(10 - 1) = 2^9 = 512 nickels.

But because 1 nickels = 5 cents

512 nickels = 5 × 512 = 2560 cents.

Answer 2

Explanation:

If the initial amount of nickel is doubling in value each day, it means that the amount of nickel is increasing in geometric progression. The formula for determining the nth term of a geometric sequence is expressed as

Tn = ar^(n - 1)

Where

n represents the common ratio

a represents the first term of the sequence (initial amount)

n represents number of terms in the sequence (days)

r represents common ratio between consecutive terms(days)

From the information given,

r = 2

n = 10

a = 0.05

Therefore, for 10days, T10

T10 = 0.05 × 2^(10 - 1)

T10 = 0.05 × 2^9

T10 = 25.6