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# If interest on a savings account is paid monthly at an annual rate of

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
If interest on a savings account is paid monthly at an annual rate of  [#permalink]

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06 Feb 2018, 02:12
00:00

Difficulty:

15% (low)

Question Stats:

85% (01:37) correct 15% (01:32) wrong based on 46 sessions

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If interest on a savings account is paid monthly at an annual rate of 25/4 percent and if the interest is not reinvested, then in how many years will the total amount of interest earned equal the amount of money saved in the account?

(A) 36

(B) 24

(C) 18

(D) 16

(E) 12

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If interest on a savings account is paid monthly at an annual rate of  [#permalink]

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06 Feb 2018, 02:31
1
Bunuel wrote:
If interest on a savings account is paid monthly at an annual rate of 25/4 percent and if the interest is not reinvested, then in how many years will the total amount of interest earned equal the amount of money saved in the account?

(A) 36

(B) 24

(C) 18

(D) 16

(E) 12

Since the annual rate is $$\frac{25}{4}$$ percent,
we will recover $$\frac{25}{4}*\frac{1}{100} = \frac{25}{400} = \frac{1}{16}$$th of the total money invested every year.

Since, the interest is not re-invested, it will take 16 years to recover the amount such that
the total amount of interest earned is equal to amount of money invested.(Option D)
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Re: If interest on a savings account is paid monthly at an annual rate of  [#permalink]

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06 Feb 2018, 05:08
1
Bunuel wrote:
If interest on a savings account is paid monthly at an annual rate of 25/4 percent and if the interest is not reinvested, then in how many years will the total amount of interest earned equal the amount of money saved in the account?

(A) 36

(B) 24

(C) 18

(D) 16

(E) 12

As the calculation looks straightforward, we'll just do it.
This is a Precise approach.

We receive 25/4 percent interest per year and are asked when this equals the bulk of our savings, or 100%.
So, we're asked to solve the equation (25/4)*x = 100
This gives x = (100*4)/25 = 4*4 = 16.
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Re: If interest on a savings account is paid monthly at an annual rate of  [#permalink]

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08 Feb 2018, 15:40
Bunuel wrote:
If interest on a savings account is paid monthly at an annual rate of 25/4 percent and if the interest is not reinvested, then in how many years will the total amount of interest earned equal the amount of money saved in the account?

(A) 36

(B) 24

(C) 18

(D) 16

(E) 12

Because the interest earned is not reinvested, we can use the formula for simple interest: I = P x r x t, where P is the original amount invested, r is the interest rate, and t is the number of years.

We want to calculate the number of years it takes for the earned interest to equal the original principal invested, so we have P = P x r x t:.

P = P x (25/4)/(100) x t

1 = 25t/400

400 = 25t

16 = t

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Re: If interest on a savings account is paid monthly at an annual rate of  [#permalink]

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10 Feb 2018, 04:26
Bunuel wrote:
If interest on a savings account is paid monthly at an annual rate of 25/4 percent and if the interest is not reinvested, then in how many years will the total amount of interest earned equal the amount of money saved in the account?

(A) 36

(B) 24

(C) 18

(D) 16

(E) 12

Option D

Given : Interest =Amount
=> $$\frac{PRT}{100}=P$$
=> $$\frac{25T}{4*100}=1$$
=> T =16 Years
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Re: If interest on a savings account is paid monthly at an annual rate of   [#permalink] 10 Feb 2018, 04:26
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