Question

Algebraically manipulating the formula FV = P(1 + n) find the principal P (to the nearest whole cent) that needs to be deposited in the bank for Joseph to have afuture value FV of $8,000 in his account in 5 years with an interest rate of 6%, compounded annually.$6,123.97$4,994.33$7,012 25$5,978.07None of these choices are correct.

Answer 1

`FV=P(1+r)^t`

Algebraically manipulating the formula, by making the principal P the subject of the formula, we have;

`P=(FV)/((1+r)^t)`

Given:

`\begin{gathered} FV=\text{ \$8,000} \\ t=5\text{years} \\ r=6\text{ \% =}(6)/(100)=0.06 \\ \end{gathered}`

Substituting all these values in the newly generated formula, we have;

`\begin{gathered} P=(FV)/((1+r)^t) \\ P=(8000)/((1+0.06)^5) \\ P=(8000)/(1.06^5) \\ P=(8000)/(1.338) \\ P=\text{ \$5978.07} \end{gathered}`

Therefore, the principal that needs to be deposited in the bank is $5978.07 to the nearest cent