Question

1. Richard has to invest the $12,000 he got from hisgrandmother. Part of the money is invested in hissavings account with an interest rate of 3.25% and theother part is invested at 11% in non-insured bonds. IfRichard earned $1010 in interest over the past year,how much did he put into savings and how much wasput into uninsured bonds?

Answer 1

Given,

Total amount invested by Richard is $12000.

Consider,

Part of money invested by Richard in saving account is x.

Part of money invested by Richard in non-insured bonds is 12000-x.

Here,

The rate of interest for the saving account is 3.25%.

The rate of interest for the non-insured bond is 11%.

The total interest earned by Richard is $1010.

The expression for the simple interest is,

`\text{simple interest=}(P* R* T)/(100)`

Here,

P=princpal=$12000

R=rate of interest =3.25% and 11%

T=time=1 year.

Substituting the values in the expression,

`\begin{gathered} (x*3.25*1)/(100)+(12000-x*11*1)/(100)=1010 \\ (3.25x)/(100)+(132000-11x)/(100)=1010 \\ 132000-11x+3.25x=101000 \\ 132000-7.75x=101000 \\ 132000-101000=7.75x \\ x=(31000)/(7.75) \\ x=4000 \end{gathered}`

Hence, the amount invested by the Richard in saving account is 4000.

Part of money invested by Richard in non-insured bonds is 12000-x.

`\text{part of non-insured =12000-4000=8000}`

Hence, the amount invested by the Richard in non-insured bonds is 8000.

Hence, the part of amount invested in saving account is $4000 and the part of amount invested in non-insured bonds is $8000.