Compound Interest #6-7

Question

$4800 is invested at 3.2% APR compounded semiannually.
Use the compound interest formula to compute the balance in the account after 14 years.

Balance =____$ (Round to the nearest cent.)

 $4800 is invested at 3.2% APR compounded continuously.
Use the compound interest formula to compute the balance in the account after 14 years.

Ballance = ____$ (Round to the nearest cent.)

Answer 1

For 3.2 % Annual Percentage Rate (APR), compounded semi-annually (or twice a year), construct the formula

Balance Equals Principal Times (One Plus APR Divided By Compounding Periods Per Year) Raised To The Power Of (Number Of Years Times Number Of Compounding Periods Per Year).

For conditions given here, one obtains B = 4800(1 + .032/2)^(14×2) equivalent to $7486.26.

For the same conditions along with Continuous Compounding, one would determine the Limit of

B = 4800(1 + .032/N)^(14×N) as N goes to Infinity (or grows extremely large). An Online Limit Calculator

gives this Limit as equivalent to $7512.82.

A Casio Programmable Calculator shows that B reaches 7512.82 at N = 1418.