Question

Investigate the difference between compounding annually and simple interest

for parts a-j. Round to the nearest cent.

a. Find the simple interest for a 1-year CD for $5,000 at a 2.5% interest rate.

b. Find the interest for a 1-year CD for $5,000 at an interest rate of 2.5%,

compounded annually.

c. Compare the results from parts a and b.

d. Find the simple interest for a 3-year CD for $5,000 at an interest rate

of 2.5%.

e. Find the interest for a 3-year CD for $5,000 at an interest rate of 2.5%,

compounded annually.

f. Compare the results from parts d and e.

g. Find the simple interest for a 6-year CD for $5,000 at an interest rate of 2%.

h. Find the interest for a 6-year CD for $5,000 at an interest rate of 2%,

compounded annually.

i. Compare the results from parts g and h.

j. Is interest compounded annually the same as simple interest? Explain

Answer 1

Explanation:

Simple interest formula

`A = P (1 + rt)`

Compound interest formula

`A = P(1 + (r)/(n))^(nt)`

a.

`A = 5000 (1 + 0.025*1)\\A=5000(1.025)\\A=5125`

Simple interest is $125

b

.
`A = 5000 (1 + (0.025)/(1))^(1*1) \\A=5000(1.025)\\A= 5125`

Compound interest is $125

c. the result for both a and b are the same

d.

`A = 5000 (1 + 0.025*3) \\A=5000(1.075) \\A=5375`

the simple interest is $375

e

.
`A = 5000 (1 + (0.025)/(1))^(1*3)] \\A=5000(1.025)^3 \\A=5000(1.077)\\A= 5385`

the compound interest is $385

f. the result compared, compound interest is $10 more than simple interest

g.

`A = 5000 (1 + 0.02*6) \\A=5000(1.12) \\A=5600`

the simple interest is $600

h.

`A = 5000 (1 + (0.02)/(1))^(1*6)] \\A=5000(1.12)^6 \\A=5000(1.9738) \\A= 9869`

the compound interest is $4869

i. the result from g and h, h is over 8 times bigger than g.

j. interest compound annually is not the same as simple interest, only for the case of a and b seeing that it is for 1 year. but for 2years and above there is difference as seen in c to h