Question

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

Future amount needed - $6,000

Interest rate - 2%

Compounding period - semi annually

Investment time - 2 years

i Present Value of $1.00 Rate per period Periods 0.5% 1% 1.5% 2% 2.5% 3% 4% 5% 6% 8% 10% 12% 0.99502 0.99010 0.98522 0.98039

Answer: The present value is $ . (Round to the nearest cent as needed.)

Answer 1

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

Explanation:

This is a compound interest problem

Compound interest formula:

The compound interest formula is given by:

`A = P(1 + (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 + (0.02)/(2))^(2*2)`

`6,000 = 1.0406P`

`P = $5765.90`

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