Question

Suppose you have $ 12,000 to invest. Which of the two rates would yield the larger amount in 5 years :11 % compounded quarterly or 10.85 %compounded continuously?

Answer 1

FV of $12000 if compounded quarterly @11% after 5 Years:

FV = Deposit * (1+r)ⁿ

where r is int rate per quarter & n is no. of quarters

= $ 12,000 * (1+0.0275)²⁰

= $ 12,000 * (1.0275)²⁰

= $ 12,000 * 1.7204

= $ 20,645.14

FV of $12000 if compounded continously @10.85% after 5 Years:

FV = Deposit * e^rt

where r is Int rate per anum & t is no.of years

= $ 12,000 * e^{0.1085 * 5}

= $ 12,000 * e^0.5425

= $ 12,000 * 1.7202

= $ 20,642.47

Almost both are giving same amount, 11% compounded is giving $ 3 extra , it may be because of rounding off diff.

Pls comment, if any further assistance is required.