Question

Evelyn invests $5,000 in a savings account that pays interest at a rate of 6.7% compounded annually. If she withdraws half the interest earned at the end of the third year, approximately how much additional interest does she earn during the fourth year

Answer 1

$371

Explanation:

The computation of additional interest during the fourth year is shown below:

but before that we need to do the following calculations

Amount = Principal × (1 + (rate of interest ÷ (1 × 100)))^(1 × number of years)

A = $5,000 × (1 + (6.7% ÷ (1 × 100)))^(1 × 3)

= $5,000 × (1 + (6.7 ÷ 100))^(1 × 3)

= $5,000 × (1 + 0.067)^3

= $5,000 × (1.067)^3

= 5000 × 1.214

= $6,070

Now, Interest gained after 3 years on the amount of Principal is

= $6,070 - $5,000

= $1,070

Here Evelyn issued interest which is half that is earned at the end of the 3rd year

Sp,

Half of the interest gained will be

= $1,070 ÷ 2

= $535

Now,

The new Principal amount for 4th year is

= $6,070 - $535

= $5,535

So, the final amount in the fourth year is

A = P × (1 + (r ÷ n))^(nt)

= $5,535 × (1 + 0.067 ÷ 1 ]^(1 × 1)

= $5,535 × 1.067

= $5.905.845

Hence the additional interest in the fourth year is

= $5,905.845 - $5,535

= $370.845

or

= $371

Therefore for computing the additional interest during the fourth year we simply applied the above formula.