Alan has split his savings equally into two accounts.

[BTGmoderatorDC]

Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined

What formula should i use in figuring the correct Option in this problem? Can some experts help?

OA D

[Jay@ManhattanReview]

Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined

What formula should i use in figuring the correct Option in this problem? Can some experts help?

OA D

Let's tackle this one without using any formulae.

Let's first talk about the first account (Simple interest saving account).

Interest in the first year = 22%;
Interest in the second year = 22%; Interest does not compound in case of simple interest.

Total interest in two years = 2*22% = 44%

Now, let's talk about the second account (Compound interest saving account).

Interest in the first year = r%;
Interest in the second year = r% + (r% of r%); Interest gets compounded in case of compound interest.

Total interest in two years = r% + (r% + r% of r%) = 2r% + r%*r% = r%(2 + r%)

We know that after two years, the interests are same from both the accounts, thus,

44% = r%(2 + r%)

44 = r(2 + r/100)

Solving for r would involve handling a quadratic equation, which may be time-consuming. Let's think of another approach.

Let's plug-in the values from the options. Since option D = 20 is the easiest one to handle, let's try this first.

@r = 20, the value of r(2 + r/100) = 20(2 + 20/100) = [20*2 + (20*20/100)] = 40 + 4 = 44%. It matches the desired result. Thus, option D is the correct answer.

The correct answer: D

Hope this helps!

-Jay

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[GMATGuruNY]

Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?

A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined

Let the savings in each account = 100.

In the account with simple annual interest of 22%:
Total after the first year = 100 + (22% of 100) = 100+22 = 122.
Total after the second year = 122 + (22% of 100) = 122+122 = 144.

For the account with r% COMPOUNDED annual interest, we can PLUG IN THE ANSWERS, which represent the value of r.
After two years, the account with compounded annual interest must hold $144 -- the same amount yielded by the account with simple annual interest.

D: 20%
Total after the first year = 100 + (20% of 100) = 100+20 = 120.
Total after the second year = 120 + (20% of 120) = 120+24 = 144.
Success!

The correct answer is D.