An initial deposit of $26,000 grows at an annual rate of 7% for 20 years. Compare the final balances resulting from continuous compounding and annual compounding. Round the answers to the nearest cent.
A) $100,610.89 from annual compounding; $105,433.70 from continuous compounding
B) $100,611.80 from annual compounding; $105,435.20 from continuous compounding
C) $100,613.85 from annual compounding; $105,455.20 from continuous compounding
D) $100,608.80 from annual compounding; $105,437.25 from continuous compounding

Question

Quizplus · Accepted Answer

For annual compounding, we use the formula A=P(1+r/n)^(n*t), where P= $26,000, r=0.07, n=1 (annual compounding) and t=20.
A= $26,000(1+0.07/1)^(1*20)= $100,611.80.

For continuous compounding, we use the formula A=Pe^(r*t), where P= $26,000, r=0.07, and t=20.
A= $26,000e^(0.07*20)= $105,435.20.

Therefore, the final balance resulting from continuous compounding is higher than that from annual compounding. The closest option to this answer is B.

An Initial Deposit of $26,000 Grows at an Annual Rate