Dayo plans to invest a certain amount of money in a savings account th

Question

Dayo plans to invest a certain amount of money in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Dayo will need to invest in order to earn more than $100 in total interest during the first two quarters after the investment is made?

A. $1,500
B. $1,750
C. $2,000
D. $2,500
E. $3,000

A. $1,500
B. $1,750
C. $2,000
D. $2,500
E. $3,000

carcass · Accepted Answer

OE

You can use the compound interest formula (if you have it memorized) to solve, but glance at the answers. They're decently far apart. Plus, the question asks for an approximate answer. Estimate!

Dayo's interest rate is 8% annually, but compounded quarterly. In other words, each quarter, Dayo will earn 2% interest (and that adds up to the total 8% over the course of four quarters, or a full year).

The problem asks about the first two quarters, so Dayo will earn 2% in each of those quarters. But how can you figure out what the starting investment amount was without writing a complicated equation?

This problem is asking you to solve for the starting point—in the real world, the first thing you'd figure out is how much you were going to invest. When the problem asks you to solve for the "real world" starting point, then that starting point is somewhere in the answer choices. So Work Backwards! Try the answers to find the one that works. (And estimate—quick and dirty for the win.)

This problem tosses in a twist: It asks for the minimum that Dayo will have to invest. In other words, more than one answer may result in Dayo earning more than $100 in interest, but only one of those answers will be the minimum value. In order to minimize (no pun intended) the number of answers you have to try, start somewhere in the middle with a number that looks easy to work with.

(C) $2,000
Dayo earns 2% of $2,000 in the first quarter. Find 1% of 2,000 and double it: $2,000 becomes $20 becomes $40. So Dayo earns $40 in the first quarter and now has a total of $2,040 in the bank. In the second quarter, Dayo again earns 2%, but the new starting number is $2,040 rather than $2,000. How does that affect the amount of interest Dayo earns?

It increases it very slightly. Dayo earns $40 plus a little bit in the second quarter, for a total of $80 and a little bit. The problem wants Dayo to earn at least $100, so this isn't enough. Eliminate answers (A), (B), and (C).

Since the problem asks for the minimum, try the next higher value.

(D) $2,500
Dayo earns 2% in the first quarter: 1% of 2,500 is 25, so 2% is 50. In the second quarter, Dayo will earn $50 plus a little bit. Total interest earned is 50 + 50 + a little bit, which is more than $100. Since answer (E) is greater, it will work too, but it can't be the minimum, since (D) works. Eliminate (E).

The correct answer is (D).

Tip: When working backwards from the answer choices, take a moment to think about where you want to start, based on the details of the problem. If you do, most of the time, you won't have to try more than two answer choices. In this case, if (D) hadn't worked, then you'd have known that (E) was the correct answer without having to try it.

sarthak1701 · Answer

Don't get bogged down into compounding, essentially you are only compounding once, and the annual rate is 8% so we can estimate since the choices are fairly spread apart.

The interest per quarter will be 2%.

Let's check the choices.

A 1500, one quarter's interest = 30, and 2 quarters' interest will be a little more than 60, which is much less than our required amount of 100. Let's jump to a higher number.

C 2000, 2% = 40, 2 quarters' interest is a little more than 80, again not close to 100

D 2500, 2% = 50, 2 quarters' interest is a little more than 100, This might be the correct answer.

E 3000, 2% = 60, 2 quarters' interest is more than 120, reject this option.

Ans. D

gmatophobia · Answer

In the first quarter, the interest earned using simple interest and the interest earned using compound interest is the same. Let's find out the interest earned at the end of the first quarter.

The most friendly number that we see in the option is $2000, so let's start with that. We will use the formula of simple interest to calculate the interest amount -

Interest earned at the end of the first quarter =  $2000 * \frac{8 }{ 400} = 5*8 = $40

Therefore in the second quarter, the interest earned will be $40 (i.e. the interest from $2000) + interest on the interest of the first quarter ⇒  $40 * \frac{8 }{ 400} = $0.80

Total interest = $40 + $40 + $0.80 = $80.80

The cumulative interest amount is less than $100, hence we can conclude that Dayo needs to deposit more than $2000 to earn more than $100 in total interest during the first two quarters.

Let's assume that Dayo deposits $2500

Interest earned by the end of the first quarter =  $2500 * \frac{8 }{ 400} = 25*2 = $50

As the interest in one quarter is $50, the interest in the second quarter will be more than $50. Hence, we can infer that the cumulative interest by the end of the second quarter will be more than $100. Hence, from the given options the minimum amount that Dayo needs to invest in order to earn more than $100 in total interest during the first two quarters after the investment is made is $2500.

Option D

abcd1234!! · Answer

P  - P >= 100 (formula for CI compounded quarterly with 2 quarters gone i.e 6 months or 1/2 year)

P  >= 100
P  >= 100
P  >= 100
P(101/50)(1/50) >= 100
P >= (100 * 50 * 50)/101
P >= 2475.24

option (D)

Armaan209 · Answer

Solution in 30 Seconds : 8% interest in annual , so 2% quaterly.
 After 1st month we would have

X + 0.02X

After Second Month we would have

X +0.02X( from previous month) + 0.02x ( Simple interest) + (0.02x)(0.02) = ( Interest on interest) ( In fractions this does not looks scary

X ( we can ignore because we donot want the whole value, only the interest is being asked

2/10 x + 2/10x + 4/100x = 100 
4/10x + 4/100X = 100
400x+4x = 10000
x = 10000/404

shubhim20 · Answer

from where did you get -p at end in 1st step and how did it get to -1

shubhim20 · Answer

Bunuel  please explain this in detail

Bunuel · Answer

When requesting a solution in a thread that already has a couple of detailed responses, please explain what exactly is unclear to you. That way, I can address your specific confusion directly. This also helps keep the discussion focused and constructive, reduces unnecessary repetition, and makes it easier for others to follow along and contribute meaningfully.

Thank you!

Dayo plans to invest a certain amount of money in a savings account th

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