Question

If an investment over eight years at a rate of $160.00 results in a final balance of $660.00, what was the original investment?

Answer 1

Answer:

The original investment was approximately $222.73.

Step-by-step explanation:

Given :

Time = 8 years

Rate of Interest = $160.00

Final Balance = $660.00

To Find:

The value of the original investment

Calculations:

We can solve this problem by using the formula for compound interest:

$A =P(1 +\frac{r}{n} )^{nt}$

where:

A is the final balance

P is the principal (original investment)

n is the number of times the interest is compounded each year,

r is the yearly interest rate (expressed as a decimal).

t is the time (in years)

We are given that the investment was made for 8 years, and resulted in a final balance of $660.00. We are also told that the interest rate is $160.00, but we need to convert this to a decimal and find the annual interest rate. Dividing the interest by the time and number of years, we get:

$r = \frac{160}{8 \times 1} = 20$

So the annual interest rate is 20%.

We don't know the original investment (P), so we'll use that as our variable. Using the formula with the given values as substitutes, we obtain:

$660 =P(1 +\frac{20}{1} )^{1 \times 8}$

Simplifying:

$660 =P(1.20)^{8}$

Dividing both sides by $P(1.20)^{8}$

$P =\frac{660}{P(1.20)^{8}}$

Using a calculator, we get:

P ≈ $222.73

Therefore, the original investment was approximately $222.73.

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