Question

A bank offers a CD that pays a simple interest rate of 7.0​%. How much must you put in this CD now in order to have ​$2 comma 000 for a​ home-entertainment center in 5 years. The present value that must be invested to get ​$2 comma 000 after 5 years at an interest rate of 7.0​% is ​$

Answer 1

Answer: The present value that must be invested is $1,481.48

Explanation: The simple interest payable has been give as 7% (that is 0.07), the time in years is 5, and at the end of that period and at that rate, the amount woukd have become 2000.

Therefore we need to calculate the amount such that when added to the interest, both sum up to 2000. That is, Principal plus Simple interest equals 2000.

The formular for simple interest is given as follows;

I = P x R x T

Note that the principal and interest is yet unknown, but both adds up to 2000. Therefore;

I + P = (P x R x T) + P

Where I + P = 2000, R = 0.07 and T = 5

(Note that P has been added to the Interest and hence has been added to the right hand side of the equation as well. Rule of algebra, whatever happens to the left hand side must equally be done to the right hand side of any equation)

2000 = (P x 0.07 x 5) + P

2000 = 0.35P + P

2000 = 1.35P

Divide both sides of the equation by 1.35

1481.481 = P

**A quick check would reveal the following**

I = P x R x T

I = 1481.481 x 0.07 x 5

Interest = 518.518

Principal + Interest = 2000

1481.481 + 518.518 = 2000

1999.999 ≈ 2000

Therefore the amount of principal that must be invested is $1481.48

Answer 2

In order to have $2,000 in five years time $1481.48 must be invested today at 7.0% simple interest

Step-by-step explanation:

The amount to invest in the CD now can be computed using the present value formula,which is given below:

A=P*(1+rn)

P=A/(1+rn)

A is the future value which is expected cash flow in 5 years time i,e $2000

r is the rate of return on the CD which is 7.0%

n is the number of years the funds would be placed in the CD and that is 5 years

P=$2000*(1+7.0%)^-5

P=$2000/1+(0.07*5)

P=$2000/(1+0.35)

P=$2000/1.35

P=$1481.48