how do I solve this?

Question

Carl deposited P dollars into a savings account that earned 8 percent annual interest, compounded semiannually. Carl made no additional deposits to or withdrawals from the account. After one year, the account had a total value of $10,816. What was the value of P ?

Answer 1

Compound Interest Formula

A=P(1+(r⁄n))^nt

 

A=Amount

P=Principal

r=rate of interest

n=number of times the interest is compounded per year

t=time in years

 

A=$10,816

P=unknown you are trying to solve for

r=8%=0.08

n=2, since the interest is compounded semiannually=twice a year

t=1, since the $10,816 total was after a year of interest

 

Now you simply plug in all these known values and solve for P

 

$10,816=P(1+(0.08/2))^2×1

 

dividing both sides by the quantity: (1+(0.08/2))^2×1 to isolate the Principal, P

 

⇒P=$10,816/(1+(.04))²

 

⇒P=$10,816/(1.0816)=$10,000