Question

Scrooge mcduck deposits $200,000 into two simple interest accounts. The annual simple interest rate on one account is 2%. The annual simple interest on the second account is 3%. How much should be invested in each account so that the total interest earned is $5,550 at the end of one year?

Answer 1

Explanation

There are two accounts.

Let, in the account of rate 2%,

he should deposit x

So, for the account of rate 3%,

he should deposit 200000-x ,

Because the total deposits is 200000

Now, from the simple interest formula we know,

I=Pnr

where, I is the interest, P is the capital,

n is the time and r is the rate.

So, for the account of 2% rate , we get

r=2%=2/100=0.02

n=1 year

P=x

So, interest,

I=Pnr

=x (1) (0.02)

=0.02 x

And for the account of rate 3% we get

I=(200000-x) (1) (0.03)

=6000-0.03x

Total interest is $5550

So,

According to question,

0.02x+6000-0.03x=5550

or, -0.01x=5550-6000

or, -0.01x=-450

or, x= -450 / -0.01

=45000

Now,

200000-45000=155000

So, he should deposit $45000 at 2% rate

and $155000 at 3% rate