Question

Find the interest earned on a $50,000 deposited for six years at 1 1/8% interest, compounded continuuously. Round to the nearest cent ______

Answer 1

The interest on the $50,000 investment for six years is approximately $3,491.51.

The compound interest formula can be expressed as:

A = P ×
`e^(rt)`

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that:

Principal P = $50,000

Compounded continuously

Time t = 6 years

Interest rate r = 1 1/8% = 1.125 = 1.125/100 = 0.01125

Accrued amount A =?

Interest I =?

First, we determine the accrued amount A:

`A = p * e^(rt)\\\\A = 50000 * e^(0.01125*6)\\\\A = 50000 * e^(0.0675)\\\\A = \$53,491.51`

Now, to determine the interest, subtract the principal from the accrued amount:

Interest = A - p

Interest = $53,491.51 - $50,000

Interest = $3,491.51

Therefore, the interest earned is approximately $3,491.51.