Question

Compare simple interest and compound interest, both at 7.5%, when $1,700 is invested for 5 years. Determine which interest earning type will result in a higher balance. Find this balance.(1 point) Responses Compound interest at 7.5% is the better earning type, with a resulting balance of $2,440.57 after 5 years of investment. Compound interest at 7.5% is the better earning type, with a resulting balance of $2,440.57 after 5 years of investment. Compound interest at 7.5% is the better earning type, with a resulting balance of $740.57 after 5 years of investment. Compound interest at 7.5% is the better earning type, with a resulting balance of $740.57 after 5 years of investment. Simple interest at 7.5% is the better earning type, with a resulting balance of $637.50 after 5 years of investment. Simple interest at 7.5% is the better earning type, with a resulting balance of $637.50 after 5 years of investment. Simple interest at 7.5% is the better earning type, with a resulting balance of $2,337.50 after 5 years of investment.

Answer 1

Compound interest at 7.5% is the better earning type, with a resulting balance of $2,440.57 after 5 years of investment.

How to calculate simple and compound interest

The formula for simple interest is I = P * r * t, where:

I is the interest earned,

P is the principal amount ($1,700 in this case),

r is the interest rate (7.5%),

t is the time period (5 years).

The formula for compound interest is

`A = P * (1 + r/n)^(n * t)`,

where:

A is the amount after t years,

P is the principal amount ($1,700),

r is the interest rate per period (7.5%),

n is the number of times the interest is compounded per year (let's assume it's compounded annually, so n = 1),

t is the time period (5 years).

Let's calculate both simple interest and compound interest over 5 years at 7.5%:

Simple Interest:

I = P * r * t

I = 1700 * 0.075 * 5

I = 637.50

Compound Interest:

`A = P * (1 + r/n)^(n * t)\\A = 1700 * (1 + 0.075/1)^(1 * 5)\\A = 1700 * (1.075)^5`

A ≈ 2440.57

Therefore, the correct response is: "Compound interest at 7.5% is the better earning type, with a resulting balance of $2,440.57 after 5 years of investment."