Question

Great Dish believes that it will need new equipment in 8 years. The equipment will cost $26,000. What lump sum should be invested today at 12%, compounded semiannually, to yield $26,000?

Answer 1

Answer:

list all the factors of the following numbers

a 50.

b 99

c 150

Answer 2

The initial principal that should be invested is $10236.2

Step-by-step explanation:

Given as :

The cost of equipment after 8 years = A = $26,000

The time period = t = 8 years

The rate of interest = r = 12% compounded semi-annually

Let The initial principal = $ p

According to question

From Compound Interest method

Amount = Principal × $(1+\dfrac{rate}{2\times 100})^{2\times time}$

Or,  A = p  × $(1+\dfrac{r}{2\times 100})^{2\times t}$

Or,  $26,000 = $p  × $(1+\dfrac{12}{2\times 100})^{2\times 8}$

Or,  $26,000 = $p  × $(1.06)^{16}$

Or,  $26,000 = $p  × 2.540

∴     p = $\dfrac{26,000}{2.540}$

i.e    p = $ 10236.2

So, The initial principal = p = $ 10236.2

Hence, The initial principal that should be invested is $10236.2 Answer