Question

An algebra student has won $100.000 in a lottery and wishes to deposit it in savings account in two financial institutions. One account pays 8% simple interest, but deposits are insured only to $50.000. The second account pays 6.4% simple interest, and deposits are insured up to $100.000. Determine whether the money can be deposited do that it is fully insured and earns annual interest of $7500.

Answer 1

Answer: $7,200

Explanation:

Maximum interest, while having full insurance, depositing $50,000 in the first financial institution at 8%. This would yield

= 8/100 * $50,000

= 0.08 * $50,000

= $4,000

Then the interest from the second financial institution would be

= 6.4/100 * $50,000

= 0.064 * $50,000

= $3,200

Summing up the interest made from each gives a maximum return of

I = I1 + I2

= $4,000 + $3,200

I = $7,200

Since the student wants full insurance coverage, the student can only earn $7,200 in interest. Not the desired $7,500.

Answer 2

Answer:

It is therefore not possible to insure and earn interest on $7500

Explanation:

Total amount deposited is $100.000 in to finance institutions given FinA and Fin B

FinA pays 8% on only deposits insured to $50.000

FinB pays 6.4% on only deposits insured to $100.00

To determine if the money can be deposited we to ain an interest of $7500

Let $x be amount deposited in FinA and $(100.000-x) be the amount deposited in FinB.

x$\leq 50.000$ thus we cant insure full amount

Annual interest is $[(8/100*x)+(6.4/100*(100.000-x)) $\leq 7500$

= (2/125*x+640)$\leq 7500$

Thus since x$\leq 50.000$

(2/125*x)$\leq$ (2/125*50.000)

(2/125*x)$\leq$8