Question

Sophie deposited money into an account in which interest is compoundedsemiannually at a rate of 4.4%. She made no other deposits or withdrawals and thetotal amount in her account after 12 years was $10,336.84. How much dd shedeposit? Round answer to nearest whole number.

Answer 1

Step 1

State the formula for the amount of compound interest

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

where;

`\begin{gathered} P=deposited\text{ money} \\ r=rate=(4.4)/(100)=0.044 \\ t=12years \\ n=2 \\ A=10336.84 \end{gathered}`

Step 2

Find how much she deposited

`10336.84=P(1+(0.044)/(2))^(2*12)`
`\begin{gathered} 10336.84=P(1.022)^(24) \\ \frac{\begin{equation*}P(1.022)^(24)\end{equation*}}{(1.022)^(24)}=(10336.84)/((1.022)^(24)) \\ P=\text{ \$6131.49382} \\ P\approx\text{ \$6131} \end{gathered}`

Hence the amount she deposited to the nearest whole number is;

`P=\text{\$6131}`