Question

Suppose that $2,000 is placed in a bank account at the end of each quarter over the next 8 years. What is the future worth at the end of 8 years when the interest rate is 12% compounded at the given intervals? (a) Quarterly (b) Monthly (c) Continuously (a) The future worth will be $ (Round to the nearest dollar) Enter your answer in the answer box and then click Check Answer 2 parts remaining Clear All Check Answer

Answer 1

a.

i = 12% / 4 = 3% per quarter

t = 8*4 = 32 quarters

Future worth = 2000*(F/A,3%,32)

= 2000 * ((1 + 0.03)^32-1)/0.03

= 2000 * ((1.03)^32-1)/0.03

= 2000 * 52.502758

= 105005.52 ~ 105006 (Nearest Dollar)

b.

i = 12%/12 = 1% per month

Effective interest rate per month = (1+0.01)^3 - 1

= (1.01)^3 - 1

= 0.030301

t = 8*4 = 32 quarters

Future worth = 2000*(F/A,3.0301%,32)

= 2000 * ((1 + 0.030301)^32-1)/0.030301

= 2000 * ((1.030301)^32-1)/0.030301

= 2000 * 52.7795427

= 105559.08 ~ 105559 (Nearest Dollar)

c.

i = 12%/4 = 3% per quarter

Effective interest rate = e^0.03 - 1

= 1.030454534 - 1

= 0.030454534

t = 8*4 = 32 quarters

Future worth = 2000*(F/A,3.0454534%,32)

= 2000 * ((1 + 0.030454534)^32-1)/0.030454534

= 2000 * ((1.030454534)^32-1)/0.030454534

= 2000 * 52.9213967

= 105842.79 ~ 105843 (Nearest Dollar)