Question

Find the future amount that should be set aside today to yield the desired future amount.

Answer 1

Answer:

We have to set aside $5765.90 to earn what we want

Step-by-step explanation:

This is a compound interest problem

Compound interest formula:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

A: Amount of money(Balance)

P: Principal(Initial deposit)

r: interest rate(as a decimal value)

n: number of times that interest is compounded per unit t

t: time the money is invested or borrowed for

Here, we want our amount after 2 years to be $6,000, with interest rate at two percent and semi annually compounding. So:

A = 6,000

P = Present value, we have to find

r = 0.02

n = 2. Semi annually compounding means that the compounding happens twice a year.

t = 2.

So:

$6,000 = P(1 + \frac{0.02}{2})^{2*2}$

$6,000 = 1.0406P$

$P = 5765.90$

We have to set aside $5765.90 to earn what we want