BTGmoderatorDC wrote: ↑

Tue Jun 09, 2020 8:22 pm

A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 100^4:105^4
E. 725:3225

OA C

Source: Veritas Prep

Interest earned in the nth year is given by

In = [p(1 + r/100)^n] – [p(1 + r/100)^(n – 1)]

I4 = [10,000(1 + 5/100)^4] – [10,000(1 + 5/100)^3]
= [10,000(1.05)^4] – [10,000(1.05)^3]
= 10,000[(1.05)^4 – (1.05)^3]
= 10,000*(1.05)^3*0.05

Similarly,

I5 = 10,000*(1.05)^4*0.05

So, the ratio of I4 to I5 = [10,000*(1.05)^3*0.05] / [10,000*(1.05)^3*0.05] = 1/1.05 = 100/105

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Tue Jun 09, 2020 8:22 pm

A bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

A. 1:5
B. 625:3125
C. 100:105
D. 100^4:105^4
E. 725:3225



OA C

Solution:

The principal that earns interest in the 4th year is the total value of the investment at the end of the third year, which is 10,000 * (1 + 0.05)^3 = 10,000 * (1.05)^3. Thus, the interest earned at the 4th year is 5% of this amount, which is 10,000 * (1.05)^3 * (0.05).

Similarly, the principal that earns interest in the 5th year is the total value of the investment at the end of the fourth year, which is 10,000 * (1.05)^4. The interest earned at the 5th year is 5% of this amount, which is 10,000 * (1.05)^4 * 0.05.

Thus, the ratio of the interest earned in the 4th year to the interest earned in the 5th year is:

[10,000 * (1.05)^3 * (0.05)]/[10,000 * (1.05)^4 * 0.05]

1/1.05

100/105

Answer: C