Question

Anna starts a fixed deposit with $178000, the bank offers 9.5% per year simple interest for 8 months. she has the option of restarting the investment using the interest earned as principal or cashing out at the end of the 8 months, (A) Calculate the interest due after 8 months. (B) if she restarts the investment into a new one calculate the total value of the investment at the end of the second 8 months

Answer 1

Using simple interest, we have that:

A) The interest due after 8 months is $11,272.33.

B) The total value of the investment will be of $189,986.24.

The amount of interest earning using simple interest, after t years, with an yearly interest rate of i and an initial investment of P is given by:

$E = Pit$

In this problem:

• Deposit of $178,000, hence $P = 178000$.
• Interest rate of 9.5% per year, hence $i = 0.095$.
• 8 months, the time is in years, hence $t = \frac{8}{12} = \frac{2}{3}$

Item a:

$E = Pit$

$E = 178000(0.095)\frac{2}{3} = 11272.33$

The interest due after 8 months is $11,272.33.

Item b:

For the second interest, we consider $P = 11272.33$, hence:

$E_2 = Pit$

$E_2 = 11272.33(0.095)\frac{2}{3} = 713.91$

The total value will be composed by:

• The initial deposit of $178,000.
• The first interest of $11,272.33.
• The second interest of $713,91.

Hence, it will be:

$T = 178000 + 11272.33 + 713.91 = 189986.24$

The total value of the investment will be of $189,986.24.

A similar problem is given at brainly.com/question/13176347