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?
Answers
Solution:
A = P[1 + (r/n)]^(nt)
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A = 5000 [ 1 + {6.7 / (1*100)}]^(1*3)
A = 5000 [ 1 + {6.7/100}]^(1*3)
A = 5000 [ 1 + 0.067 ]^3
A = 5000 [ 1.067 ]^3
A = 5000 * 1.214
A = $ 6070
Interest gained after 3 years on Principal Amount = 6070 - 5000 = $1070
She has withdrawn half of the interest earned at end of third year,
Half of interest gained = 1070/2 = $535
The new Principal amount for 4th year will be,
Principal for 4th year will be = 6070 - 535 = $5535
And the Amount of 4th year will be,
A = P[1 + (r/n)]^(nt)
A = 5535 [ 1 + 0.067/1 ]^(1*1)
A = 5535 * 1.067
A = $5905.845
The additional interest she earned during the fourth year will be,
Amount earned during 4th year = 5905.845 - 5535 = $370.845 ≈ $371
The additional interest amount earned during the fourth year is $370.845 or approximately $371