Question

Diana can either invest $20,\!000$ dollars for $4$ years with a simple interest rate of $6\%$ or an interest rate of $7\%$ which compounds quarterly. How many more dollars, rounded to the nearest dollar, would she get with the better interest rate than with the worse one?

Answer 1

Answer:

$34,243.28

Explanation:

Simple interest = P x r x t

where:

P = Principal

r = rate

T = time

Therefore simple interest = 20,000 x 6% x 4 = $4,800

Compound Interest = ((P*(1+r)^n) - P),

where P is the principal,

r is the annual interest rate = 7%, and

n is the number of periods = 4 years x 4 quarters a year.

Therefore compound interest = ((20000 (1+0.07)^16)-20000) = $39,043.28

Difference in interest = $39,043.28 - $4,800 = $34,243.28

Answer 2

Answer:

$1,599

Explanation:

Maria has two alternative investment opportunities:

investment A:

interest earned = present value x r x n = $20,000 x 6% x 4 years = $4,800

investment B:

future value = present value x (1 + r)ⁿ

• r = 7% / 4 = 1.75%
• n = 4 years x 4 = 16 quarters

future value = $20,000 x (1 + 1.75%)¹⁶ = $20,000 x 1.0175¹⁶ = $26,398.59 ≈ $26,399

interest earned = future value - present value = $26,399 - $20,000 = $6,399

the difference between the amount of interest earned = $6,399 - $4,800 = $1,599