Question

$9,400.00 is invested at an APR of 4.1% compounded semianually (twice per year). Write a numerical expression that represents the investment's value after 13 years.

Answer 1

To solve this problem we will use the formula for compound interest:

`P_N=P_0\cdot\mleft(1+(r)/(k)\mright)^(N\cdot k).`

Where:

• P_N, is the balance in the account after N years,

,

• P_0, is the starting balance of the account (also called an initial deposit, or principal),

,

• r, is the annual interest rate in decimal form,

,

• k, is the number of compounding periods in one year.

In this problem we have that:

• N = 13 (13 years),

,

• P_N is the unknown,

,

• P_0 = $9400,

,

• r = 4.1/100 = 0.041,

,

• k = 2 (because the interest compounded twice per year).

Replacing these values in the formula above, we find:

`P_(13)=9400\cdot(1+(0.041)/(2))^(13\cdot2)_{}\cong15931.85.`

Answer

`P_(13)=9400\cdot(1+(0.041)/(2))^(13\cdot2)_{}\cong15931.85.`