Question

Manuela wants to have $26,000 in 18 months. About how much should she put into an 18 month CD that earns simple interest of 5.6% a year calculated semiannually in order to reach her goal.

Answer 1

since it is simple interest, in 18 months it will earn 1.5*5.6 = 8.4%,

x + 0.084x = 26000

x = 2600/1.084 = $23,985.24

Answer 2

Manuela should put $23,985.24 into an 18 month CD.

Explanation:

Manuela wants to have $26,000 in 18 months CD that earns simple interest of 5.6% a year calculated semiannually.

Since it is simple interest so in 18 months (1.5 years) it will earn = 5.6 × 1.5 = 8.4%.

Formula for Simple interest

A = P( 1 + rt)

A = amount ( 26,000 )

P = Principal ( we have to find out )

r = Rate of interest in decimal 8.4% ( 0.084 )

t = time ( 1 )

Let the principal amount be x

Now we put the values in formula to find the value of x.

26,000 = x ( 1 + 0.084 × 1 )

26,000 = x ( 1.084 )

x =
`(26000)/(1.084)`

x = 23,985.23985 rounded to 23,985.24

Manuela should put $23,985.24 into an 18 month CD.