Question

Suppose you have $14,000 to invest. Which of the two rates would yield the larger amount in 4 years 10% compounded quarterly or 9 80% compounded continuously Which of the two rates would yield the larger amount in 4 years?

A.10% compounded quarterly
b.9.88% compounded continuously

Answer 1

To determine which investment option yields a larger amount after 4 years, we compare compound interest for a 10% rate compounded quarterly with a 9.88% rate compounded continuously by using their respective formulas and calculating the amounts.

Step-by-step explanation:

Investing $14,000 and determining which compounding rate will yield a larger amount over 4 years involves comparing compound interest with continuous compounding. For option A, 10% compounded quarterly, we use the compound interest formula A = P(1 + r/n)^(nt).

Where P is the principal amount ($14,000), r is the annual interest rate (0.10), n is the number of times interest is compounded per year (4 for quarterly), and t is the number of years (4). So we have:

A = 14,000(1 + 0.10/4)^(4*4)

For option B, 9.88% compounded continuously, the formula is A = Pe^(rt), where e is the base of the natural logarithm.

So we calculate it as: A = 14,000e^(0.0988*4). After calculating both, we can compare which amount is larger to determine which investment is better.