Question

An employee put $5,000.00 in a retirement account that offers 9% interest compounded annually. The employee makes no additional deposits or withdrawals. Which amount is closest to the interest the employee will have earned at the end of 5 years? A) $229.09 B) $450.00 C) $2,250.00 D) $2,693.12

An investor puts $2,500 into a life insurance policy that pays 8.5% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 10 years?
A) $21,250.00
B) $2,125.00
C) $212.50
D) $21.25
A preschool has a rectangular field and a rectangular playground that are similar in shape. Each dimension of the field is 3.2 times the corresponding dimension of the playground. Which statement is true?
A) The area of the field is 6.4 times the area of the playground.
B) The area of the field is 10.24 times the area of the playground.
C) The perimeter of the field is 6.4 times the perimeter of the playground.
D) The perimeter of the field is 10.24 times the perimeter of the playground.

Answer 1

1. $2693.12
2. $2125.00
3. B) The area of the field is 10.24 times the area of the playground

Explanation:

1. Each year the balance is multiplied by 1.09, so after 5 years, the balance is multiplied by 1.09^5 ≈ 1.53862395. Subtracting the original invetment amount gives the value of the interest earned.

... 5000 × 1.53862395 - 5000 = 5000 × 0.53862395

... ≈ 2693.12 . . . . matches choice D

2. The interest earned is given by the formula ...

... I = Prt . . . . . where P is the principal, r is the interest rate, and t is the time period.

Filling in the given numbers, you have ...

... I = 2500×0.085×10 = 2125 . . . . matches choice B

3. The product of length and width is the area. If both length and width are multiplied by 3.2, then the area is multiplied by 3.2×3.2 = 10.24. The appropriate choice is B.

Answer 2

1. D) $2,693.12

2. B) $2,125.00

3. B) The area of the field is 10.24 times the area of the playground.

Explanation:

1. A = P (1+r/n) ^ nt

Where A is the amount in the account

P is the principal

r is the interest rate in decimal form

n is the number of times it is compounded per year

t = the number of years

We know P=5000, r= .09 , n=1 (annually) and t=5. Substituting into the equation

A = 5000( 1+.09/1) ^(1*5)

A= 5000(1.09)^5

A =7693.12

To find the interest earned, we subtract the principal from the amount in the account

I = A - P

I = 7693.12-5000

I = 2693.12

2. For simple interest

I = PRT

I is the interest

P is the principal

r is the interest rate in decimal form

t = the number of years

We know P = 2500, r = .085 and t =10 Substituting into the equation

I = (2500)(.085)(10)

I =2125

3. The scale factor is 3.2

When we move to area, the area increase by the scale factor squared

3.2^2 = 10.24. he area of the field is 10.24 times the area of the playground.