Question

Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same.

What is the approximate new interest rate?

Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%

Answer 1

`A=250(1.025)^(4t)`

Explanation:

`A=250(1.1)^(t)`

The interest rate is 10% or 0.1

n = 1

The compound interest formula is :
`A=p(1+(r)/(n))^(nt)`

n is the number of times amount is compounded.

Lets say the interest rate were to change to being compounded quarterly.

So, here A, p will remain same, r will be divided by 4 and n will change to 4.

So, new equation will be :

`A=250(1+(0.1)/(4))^(4t)`

=>
`A=250(1.025)^(4t)`

The approximate new interest rate will be =
`10/4/100=0.025` and in percentage it is 2.50%.

Answer 2

=250(1.025)∧4t

Explanation:

Using the compound interest formula we can find the expression for the total amount that accumulates in the given time t.

A=P(1+R/n)ⁿᵇ

where A is the amount, P the principal amount, R the rate as a decimal n is the number of times it is compounded and b the time.

When compounded annually, the expression becomes

A=250(1.1)∧t

When compounded quarterly, we introduce the n in our expression.

A=250(1+0.1/4)∧4t

=250(1.025)∧4t