# GMAT Avengers Study Group: Interest Rates:

Let’s first talk about Simple Interest and Compound Interest.

**Simple Interest** – The formula for SI is principal * interest rate * time, where “principal” is the starting amount and “rate” is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate.

**Compound Interest** – The formula to calculate compound interest:

Final balance = where:

P = the principal (the initial investment).

r = the annual interest rate expressed as a decimal

c = the number of times the interest is compounded each year

n = the number of years the investment collects interest

The important thing is to make sure we know how to calculate these interests and are able to manipulate things accordingly. For example, it may be the case that we have been told to calculate the rate of the interest when everything else would have been given to us. So, it is not like that we will be asked to only calculate SI or CI. All the terms used in the formula are used interchangeably.

**IMPORTANT** – As long as there is more than one compounding period, then compound interest always earns more than simple interest. We always get more interest, and larger account value overall, when the compounding period decreases; the more compounding periods we have, the more interest we earn.

The articles that we shared on our Facebook Event Page are as follows:

*Simple and Compound Interest*by**The Princeton Review***Interest and Compound-Interest Problems*by**Grockit***Free Yourself from Calculator Math*by**Veritas Prep**

## Practice Problems

**Data Sufficiency (Sample answer choices are given below)**

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

1) If $5000 invested for one year at

ppercent simple annual interest yields $500,what amount must be invested atkpercent simple annual interest for one year to yield the same amount of dollars?(A)

k= 0.8p(B)

k= 8

2) If $24,000 invested at

xpercent simple annual interest yields an interest ofzdollars at the end of one year. How much is it necessary to invest during one year atypercent simple annual interest in order to get an interest ofzdollars?(A)

x= 4(B)

x/y= 2/3

3) If a loan of

Pdollars, at an interest rate ofrpercent per year compounded monthly, is payable innmonthly installments ofmdollars each, thenmis determined by the formulaJohn and Sue took out loans whose monthly installments were determined by using the formula above. Both loans had the same interest rate and the same number of monthly installments. John’s monthly installment was what percent of Sue’s monthly installment?

(A) The amount of Sue’s loan was 4 times the amount of John’s loan.

(B) Sue’s monthly installment was 4 times John’s monthly installment.

4) On May 1 of last year, Jasmin invested

xdollars in a new account at an interest rate of 6 percent per year, compounded monthly. If no other deposits or withdrawals were made in the account and the interest rate did not change, what is the value ofx?(A) As of June 1 of last year, the investment had earned $200 in interest.

(B) As of July 1 of last year, the investment had earned $401 in interest.

**Problem Solving**

1) An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?

(A) 3.1%

(B) 9.3%

(C) 10.0%

(D) 10.5%

(E) 12.5%

2) An investment of d dollars at k percent simple interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?

(A) 2d/3

(B) 3d/4

(C) 4d/3

(D) 3d/2

(E) 8d/3

3) A sum of $16,000 amounts to $18,400 in two years according to simple interest. What is the rate of interest?

(1) 6%

(2) 6.5%

(3) 7.5%

(4) 8%

(5) 8.5%

4) Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for a full three-year period. Approximately how much interest did she earn in the last month of this period?

(1) $239.47

(2) $714.73

(3) $2793.80

(4) $7,888.83

(5) $15,529.61

5) Marcus deposited $8,000 to open a new savings account that earned five percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in Marcuss account one year after the account was opened?

(A) $8,200

(B) $8,205

(C) $8,400

(D) $8,405

(E) $8,500

6) Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

(A) $506.00

(B) $726.24

(C) $900.00

(D) $920.24

(E) $926.24

7) A sum of money doubles itself at a compound interest in 15 years. In how may years it will become 8 times?

(A) 30 years

(B) 40 years

(C) 45 years

(D) 50 years

(E) 60 years

8) An investment of $1000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $1000 increased to $4000 by earning interest. In how many years after the initial investment was made the $1000 have increased to $8000 by earning interest at that rate?

(A) 16

(B) 18

(C) 20

(D) 24

(E) 30

9) Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?

(A) 333

(B) 383

(C) 402

(D) 433

(E) 483

## Answer Key

**Data Sufficiency**

- D, Each Statement Alone is sufficient to answer the question
- B, Statement 2 alone is sufficient to answer the question
- D, Each Statement Alone is sufficient to answer the question
- D, Each Statement Alone is sufficient to answer the question

**Problem Solving**

- E
- E
- C
- A
- D
- E
- C
- B
- C

*Make sure you check out the event Facebook page to see all the comments that were being exchanged during the live session.*

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