Problem Solving

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

Simple Interest = Principal * Rate * Time

Compound Interest = Principal * (1 + Rate/100)^ Number of Times Compounded

You didn't provide the answer choices, but I think it is FAR easier to plug in, working backwards.

Here are the choices:

(A) $2750
(B) $5500
(C) $11000
(D) $22000
(E) $44000

If we started with $2750:
2750/2 = 1375

The simple interest rate is 40%.

Compounded annually, Shawn will get 20% the first year, 20% the second year. 1375 + 275 = 2650 interest in the first year. The second year's interest = .2 * 2650 = 330.

You can see how to do the math without using the answer choices here: https://www.beatthegmat.com/total-saving ... 80615.html

romitvsingh wrote:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

$ 2750
$ 5500
$ 11000
$ 22000
$ 44000

I've included the answer choices, which would be provided by the GMAT.

For both bonds, the first-year interest is the same:
550/2 = 275.

In the second year, the additional interest earned by the compound interest bond = 605-550 = 55.
This additional interest occurs because the interest rate was applied to the 275 earned in the first year.
Thus, the interest rate for the second year = 55/275 * 100 = 20%.

Since 20% is earned each year, the simple interest rate over 2 years = 40%.
Thus, 40% of 1/2 of the correct answer choice must yield simple interest of 550.

Only answer choice A works:
.4*(1/2)*2750 = 550.

The correct answer is A.

Alternatively, once we've determined the simple interest rate, we could use algebra:
.4(.5)x = 550
x = 550/.2 = 2750.

Hi Mitch,

This additional interest occurs because the interest rate was applied to the 275 earned in the first year.
Thus, the interest rate for the second year = 55/275 * 100 = 20%.

Could you please explain the above in detail. I am a bit confused here

GmatKiss wrote:Hi Mitch,

This additional interest occurs because the interest rate was applied to the 275 earned in the first year.
Thus, the interest rate for the second year = 55/275 * 100 = 20%.

Could you please explain the above in detail. I am a bit confused here

Let's take an easy example.

Let the investment = 100.
Let the annual interest rate = 20%.
Let S = the account earning simple interest over 2 years.
Let C = the account earning 2 years interest, compounded annually.

First year:
Both S and C earn $20.

Second year:
S earns another $20.
At the end of the first year, C has $120, so in the second year C earns .2*120 = $24.
Why does C earns more $4 more?
Because, in the second year, C earns not only 20% of the initial investment but also 20% OF THE INTEREST earned in the first year:
(.2*20 = 4).

Thus, in the problem above, C earned $55 more in the second year because it earned X% OF THE INTEREST earned in the first year (275):
55 = (x/100)*275
x = 20.

Hi Vivan,
Can you explain the answer in detail