Question

You decide to invest $1,500 into a certificate of depost (CD), which is a secure bank investement option.

a.) If you choose a bank advertising a certificate of deposit with 1.2% APR compounded daily, how much money will be in this account at the end of 4 years?

b.) If you choose a bank advertising a certificate of deposit with 1.2% APR compounded monthly, how much will be in this account after 4 years?

c.) Which CD option has more money in the account at the end of 4 years and explain why.

Answer 1

Answer :

(a.) Calculation of Future Value with 1.2% APR compounded daily

Future Value = Present Value * (1 + r)n

where r is the rate of interest per period i.e 1.2%/ 365 = 0.00328767123 % or 0.00003287671

n is the number of compounding period i.e 4 * 365 = 1460

Present Value = $1500

Future Value = 1500 * (1 + 0.00003287671)1460

= 1500 * 1.049169828

= 1574.80

Note : Assuming 360 days in a year.

(b.) Calculation of Future Value with 1.2% APR compounded monthly

Future Value = Present Value * (1 + r)n

where r is the rate of interest per period i.e 1.2%/ 12 = 0.1% or 0.001

n is the number of compounding period i.e 4 * 12 = 48

Present Value = $1500

Future Value = 1500 * (1 + 0.001)48

= 1500 * 1.049145492

= 1573.718 or $1573.718 or $1573.72

(c.) CD with with 1.2% APR compounded daily gives more value due to effect of continous compounding there will be interest on interest.