Question

In order to have $4,000 two years from now, how much would you have to put into an account today, if the interest rate is 4%, compounded quarterly? $______

Answer 1

Answer:

We have to put $3693.44 into an account today.

Step-by-step explanation:

From the given information it is clear that,

Amount = $4000.

Rate of interest = 4% compounded quarterly

Time = 2 years

We need to find the principle amount.

Let the principal amount be x.

Formula for amount in compound interest is

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

where,

P is principal money.

r is rate of interest.

n is number of time interest compounded in a period.

t is number of periods.

Substitute A=4000,  r=0.04, n=4, t=2 in equation (1).

$4000=P(1+\frac{0.04}{4})^{(4)(2)}$

$4000=P(\frac{101}{100}​)^{8}$

$4000=1.083P$

Divide both sides by 1.083 both sides.

$\frac{4000}{1.083}=P$

$P\approx 3693.44$

Therefore, we have to put $3693.44 into an account today.