Question

how much money should be deposited today in the account that are 7%, compounded and semi-annually so they will accumulate to 11,000 in 3 years

Answer 1

The rule of the compound interest is

`A=P(1+(r)/(n))^(nt)`

A is the new amount

P is the initial amount

r is the rate in decimal

n is the number of the periods per year

t is the number of years

Since the rate is 7% compounded semi-annual, then

r = 7/100 = 0.07

n = 2

Since the amount after 3 years will be $11 000, then

A = 11 000

t = 3

Substitute them in the rule above to find P

`\begin{gathered} 11000=p(1+(0.07)/(2))^(2(3)) \\ 11000=p(1.035)^6 \end{gathered}`

Divide both sides by (1.035)^6 to find P

`\begin{gathered} (11000)/((1.035)^6)=P \\ 8948.507087=P \end{gathered}`

Round it to the nearest cent (2 decimal places)

P = $8948.51

The amount invested was $8948.51