Question

Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 2) Suppose that you have $8000 to invest. Which investment yields the greater return over 6 years: 6.25% compounded continuously or 6.3% compounded semiannually? 2) A) $8000 invested at 6.3% compounded semiannually over 6 years yields the greater return. B) $8000 invested at 6.25% compounded continuously over 6 years yields the greater return. C) Both investment plans yield the same return.

Answer 1

Answer: A

Compound interest simply defined as the interest added at regular interval. Compound interested can be calculated using

Compound interest = P (1+) ^nt and Pe ^rt

P = Initial balance

r = Annual interest rate

n = Number of times the interest is compounded per year

t =Number of year money is invested

Using

Compound interest = P (1+ ) ^nt

Continuous

P= $ 8000

t = 6

r = 6.25%

=

= 0.0625

n = 1

Compound interest = 8000 (1+) ^1×6

= 8000 (1 + 0.0625) ^6

= 8000 (1.0625) ^ 6

= 8000× 1.4387

= $11,509.6

Semi- annually

P= $ 8000

t = 6

r = 6.3%

=

= 0.063

n = 2

Compound interest = 8000 (1+) ^2×6

= 8000 (1 + 0.063) ^12

= 8000 (1.063) ^12

= 8000× 1.4509

= $11,607.0

Investing $ 8000 semi-annually at 6.3% for 6 years yields greater return

Therefore the answer is (A)