Question

Alyssa would like to have $450,000 in her stock market account before buying a new car. She is planning to invest in a stock market account that earns 10.0%, but it charges a 0.5% front-end load fee. How much will she need to invest now in order to reach her $450,000 goal in 6 months? Round your answer to the nearest penny.

Answer 1

Front-end load fee means require to pay fee at the time of investment.

so we assume that Alyssa invested 'A'

So Front end fee = A x 0.5% = 0.005A

So $450,000 earnd by invested money = A - 0.005A = 0.995A

Earn on return = 0.995A x 10% x 6/12 = 0.04975A

Total Earning on Investment of A = 0.995A + 0.04975A = 1.04475A

So,

1.04475A = $450,000

A = $430,725.05

So Alyssa need to invest = $430,725.05

or

We calculate in other way

$450,000 after the investment amount and return

So amount require to earn =$450,000/(1+rxt) (Where: r = Return earn and t = time)

= $450,000 / (1+0.10x6/12)

= $450,000 / (1+0.05)

= $450,000 / 1.05

= $428,571.43

This amount after, the Front-end fee

Investe amount = $428,571.43 / (1-0.005) = $428,571.43 / 0.995 = $430,725.05

Alyssa need to invest = $430,725.05