Compound Interest

Show your work for each problem.

1.
In the compound interest formula , what does the exponent represent?
1. a)Interest rate
2. b)Time in years
3. c)Principal
4. d)Total amount
Answer: Time in years
In , the exponent represents time in years. Each year, your money is multiplied by , so after years, you multiply times.
2.
Calculate (round to 4 decimal places).
Answer: 1.1025
. This is the growth factor for 2 years at 5%.
3.
You invest 1000 dollars at 4% compound interest for 1 year. How much will you have?
1. a)1040 dollars
2. b)1400 dollars
3. c)40 dollars
4. d)1004 dollars
Answer: 1040 dollars
dollars. For 1 year, compound and simple interest give the same result.
4.
Calculate the final amount: 500 dollars at 6% compound interest for 2 years.
Answer: 561.80
1. What is (1 + 0.06)? 1.06
2. Calculate 1.1236
3. Multiply: 500 × 1.1236 = ? 561.80
5.
What is ? Round to 4 decimal places.
Answer: 1.2597
(rounded).
6.
You invest 2000 dollars at 5% compound interest for 4 years. What is the final amount?
Answer: 2431.01
1. What is (1 + r)? 1.05
2. Calculate (use calculator) 1.2155
3. Multiply: 2000 × 1.2155 = ? 2431.01
7.
1000 dollars invested at 7% compound interest for 5 years. What is the interest earned? Round to the nearest dollar.
Answer: 403
. Interest = dollars (rounded).
8.
Compare: 3000 dollars at 6% for 3 years. How much MORE does compound interest earn than simple interest?
1. a)573 dollars
2. b)33 dollars
3. c)540 dollars
4. d)3573 dollars
Answer: 33 dollars
Simple: . Compound: , interest = 573.05. Difference: dollars.
9.
You invest 5000 dollars at 8% compound interest for 6 years. Find the total interest earned.
Answer: 2934
1. Calculate (use calculator) 1.5869
2. Find final amount: 5000 × 1.5869 = ? 7934
3. Calculate interest: 7934 - 5000 = ? 2934
10.
Which grows faster: 1000 dollars at 10% for 5 years (compound) or 2000 dollars at 5% for 5 years (compound)?
1. a)2000 dollars at 5% gives more (2553 dollars)
2. b)They give the same amount
3. c)Cannot determine
4. d)1000 dollars at 10% gives more (1611 dollars)
Answer: 2000 dollars at 5% gives more (2553 dollars)
Option A: . Option B: . The larger principal wins even with lower rate.
11.
You want 15000 dollars in 10 years. At 6% compound interest, how much must you invest now?
Answer: 8375
1. Write the rearranged formula: P = ? A / (1+r)^t
2. Calculate 1.7908
3. Divide: 15000 ÷ 1.7908 = ? 8375
12.
10000 dollars grows to 16289 dollars in 10 years with compound interest. What was the annual rate? Give answer as percentage.
Answer: 5%
. Taking 10th root: , so .
13.
The Rule of 72: To estimate doubling time, divide 72 by the interest rate. At 8%, approximately how many years to double your money?
1. a)12 years
2. b)72 years
3. c)9 years
4. d)8 years
Answer: 9 years
Rule of 72: years. This is an approximation - the actual time is about 9.01 years.
14.
You have 500 dollars credit card debt at 18% compound interest. If you make no payments for 4 years, how much will you owe?
Answer: 970
1. What is (1 + 0.18)? 1.18
2. Calculate 1.939
3. Multiply: 500 × 1.939 = ? 970
15.
Why does compound interest grow faster than simple interest over time?
1. a)The rate increases each year
2. b)Simple interest has a cap
3. c)The principal changes each year
4. d)You earn interest on previously earned interest
Answer: You earn interest on previously earned interest
With compound interest, each year's interest is added to the principal, so you earn interest on a growing base. This creates exponential growth.