Investing inhertance.Norman invested one-half of his inheritance in a CD that had a 10% annoul yield. He lent one-quarter of of his inheritance to his brother -in-law at 12% simple interest. His income from these two investments was $6400 for 1 year. How much was the inheritance?
.10(x/2) + .12(x/4) = 6400
x = 80,000
ded
Let's solve the problem step by step:
Let's assume the total inheritance amount as "x".
Norman invested one-half of his inheritance, so he invested (1/2)x.
This investment earned him an annual yield of 10%, which can be expressed as (1/10) * (1/2)x = (1/20)x.
Norman also lent one-quarter of his inheritance, so he lent (1/4)x.
This loan earned him a simple interest of 12%, which can be expressed as (12/100) * (1/4)x = (3/25)x.
The total income from these two investments for one year was $6400. So, we can write the equation as:
(1/20)x + (3/25)x = $6400
Combining the fractions, we get:
(5/100)x + (12/100)x = $6400
(17/100)x = $6400
To isolate x, we can multiply both sides of the equation by (100/17):
x = ($6400) * (100/17)
x = $37,647.06
Therefore, the inheritance amount was approximately $37,647.06.
To find the amount of the inheritance, we need to set up equations based on the given information.
Let's assume that the total inheritance amount is X.
According to the given information:
Norman invested one-half of his inheritance in a CD at a 10% annual yield, so this investment would be (1/2) * X * 10/100 = X/20.
Norman lent one-quarter of his inheritance to his brother-in-law at a 12% simple interest, so this investment would be (1/4) * X * 12/100 = 3X/100.
The total income from these two investments for one year is $6400, so our equation becomes:
X/20 + 3X/100 = 6400.
To solve the equation, we need to find a common denominator for the fractions:
(5X + 3X)/100 = 6400.
Combining like terms, we have:
8X/100 = 6400.
To isolate X, we can cross-multiply:
8X = 6400 * 100.
Divide both sides by 8 to get the value of X:
X = (6400 * 100) / 8.
Performing the calculation, we get:
X = 80,000.
Therefore, the total inheritance amount is $80,000.