Compound Interest

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.

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

Answer 1

The compound interest formula is:

 

A = P (1 + r/f)^nf

 

P is the initial amount

A is the final amount

r is the annual interest rate (as a decimal)

f is the frequency of compounding per year

n is the number of years.

 

So in this case:

 

P = 4800

r = 3.2% or .032

f = 2, since semiannually once every HALF year, or 2 times per year

n = 14

 

So A = 4800 (1 + .032 / 2) ^14*2

 

A = $7486.26

 

 

The continuous compounding formula is

 

A = Pe^rn

 

Where e is the base of the natural logarithm (approximately 2.71828)

 

So A =4800 e^{.032 * 14}

 

A = $7,512.86