Question

a) A principal of $20,000 is invested at 6% for 10 years. Determine its future value if the interest is compounded

i. Semi-annually

ii. Monthly

iii. Continuously

iv. Explain, using your own words, the different results in (i), (ii), (iii). Explain which one the consumer would prefer, and which one the bank would prefer. 

Answer 1

i. Semi-annually:

$FV = 10,000×(1 + 0.06/2)^{2×10} = 18,061.11.$

ii. Monthly:

$FV = 10,000×(1 + 0.06/12)^{12×10} = 18,193.97.$

iii. Continuously:

$FV = 10,000×e^{0.06×10} = 18221.19.$

iv. The consumer would prefer iii, and the bank would prefer i.