Q:

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? $______

Accepted Solution

A:
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 quarterlyTime = 2 yearsWe need to find the principle amount.Let the principal amount be x.Formula for amount in compound interest is[tex]A=P(1+\frac{r}{n})^{nt}[/tex]              .... (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).[tex]4000=P(1+\frac{0.04}{4})^{(4)(2)}[/tex][tex]4000=P(\frac{101}{100}​)^{8}[/tex][tex]4000=1.083P[/tex]Divide both sides by 1.083 both sides.[tex]\frac{4000}{1.083}=P[/tex][tex]P\approx 3693.44[/tex]Therefore, we have to put $3693.44 into an account today.