COMPOUND INTEREST WORD PROBLEMS

Problem 1 :

You deposit $3500 into an account that earns 2.5% annual interest. Find the balance after one year if the interest is compounded with the given frequencies:

a. Annually:

b. Quarterly:

c. Monthly:

Solution:

Given, P = $3500, r = 2.5% = 0.025, t = 1 

a.

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

Here n = 1

A = 3500(1 + 0.025/1)¹⁽¹⁾

= 3500(1.025)

= $3587.50

b. 

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

Here n = 4

A = 3500(1 + 0.025/4)⁴⁽¹⁾

= 3500(1.00625)⁴

= $3588.32

c.

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

Here n = 12

A = 3500(1 + 0.025/12)¹²⁽¹⁾

= 3500(1.025)

= $3588.36

Problem 2 :

You deposit $500 into account that earns 1.1% annual interest. Find the balance after three years if the interest is compounded with the given frequencies:

a. Daily:

b. Semiannually:

c. Quarterly:

Solution:

Given, P = $500, r = 1.1% = 0.011, t = 3

a.

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

Here n = 365

A = 500(1 + 0.011/365)³⁽³⁶⁵⁾

= $516.78

b. 

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

Here n = 2

A = 500(1 + 0.011/2)³⁽²⁾

= 500(1.033)

A = $516.73

c. 

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

Here n = 4

A = 500(1 + 0.011/4)³⁽⁴⁾

= 500(1.033)

A = $516.75

Problem 3 :

You deposit your PFD worth $878 into a savings account that yields 0.15% (currently the rate for Alaska USA Credit Union's saving account). Suppose the interest is compounded monthly. How much money will be in the account after 4 years if you do not spend any of the money?

Solution:

Given, P = $878, r = 0.15%, t = 4

Problem 4 :

You put $500 on a credit card that charges 15% interest compounded monthly. If you do not make any payments, how will you owe a the end of 1 year?

Solution:

Problem 5 :

Your 3 1/2 year investment of $1.830 with interest of 14% which was compounded quarterly is worth how much after 3 1/2 years?

Solution:

Problem 6 :

You put $1600 on a credit card that charges 15.2% interest compounded monthly. If you make no payments for 6 months, how much will you owe?

Solution:

Problem 7 :

You deposit 50 into an account that yields 3.25% interest compounded weekly. How much money will you have after 1 year? After 10 years?

Solution:

After 1 year:

After 10 years:

Problem 8 :

You invest $5 into an account that yields 2.5% annual interest. How much will you have in your account after 2 years if the account is compounded monthly? Quarterly?

Solution:

Monthly:

Quarterly:

Problem 9 :

You put $1000 into an account that yields 1.5% compounded quarterly. How much will you have after 10 years? Use a calculator to estimate when you will have $500,000.

Solution:

After 10 years: