Question

A. Compute the balance in an account if $25,000 is invested for 5 years with an APR of 3% compounded daily. The balance in the account will be? B. For the same principal, APR, and time above, compute the balance in the account if it were compounded annually. The balance in the account will be? C. Discuss the difference in the answers above and give a possible explanation. ​

Answer 1

A. $29,045.68

B. $28,981.85

C. Compound daily applies interest everyday over a period of 365 days in a year. Compound annually only applies the 3% interest once a year.

Explanation:

3% compounded daily:

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

= 25000(1 +
`(.03)/(365)`)^365(5)

= 25000(1.00008219)¹⁸²⁵

= 25000(1.161827)

= 29045.6770

3% compounded annually:

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

= 25000(1 +
`(.03)/(1)`)^1(5)

= 25000(1.03)⁵

= 25000(1.159274)

= 28981.8518