Question

4. Suppose you deposit $100 in a savings account that compounds annually at 2%. After 1 year at this rate, the bank changes its rates of compounding to 1.5% annually. Assuming the compounding rate does not change for 4 additional years, how much will your account be worth at the end of the 5 year period?

Answer 1

Answer:

The Final amount in the account after 5 years will be $108.26

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Equations.

Since we are talking about compounding interest we can use the Exponential Growth Formula to calculate the interest over the next couple of years. The formula is the following,

$y = a*(1+r)^{t}$

Where:

1. y is the total amount after a given time
2. a is the initial amount
3. r is the interest rate in decimals
4. t is the given time

We first need to calculate the 2% interest for the first year,

$y = 100*(1+0.02)^{1}$

$y = 100*1.02$

$y = 102$

So after the first year the account will have $102. Now we can use the $102 to calculate the next 4 years of interest using the new interest rate of 1.5%

$y = 102*(1+0.015)^{4}$

$y = 102*(1.015)^{4}$

$y = 102*1.0614$

$y = 108.26$

The Final amount in the account after 5 years will be $108.26

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.