The following questions illustrate non-annual compounding. a) One hundred dollar
ID: 2722122 • Letter: T
Question
The following questions illustrate non-annual compounding.
a) One hundred dollars is placed in an account that pays 12 percent. How much will be in the account after one year if interest is compounded annually, semiannually, or monthly?
b) One hundred dollars is to be received after one year. What is the present value of this amount if you can earn 12 percent compounded annually, semiannually, or monthly?
The following questions illustrate non-annual compounding.
a) One hundred dollars is placed in an account that pays 12 percent. How much will be in the account after one year if interest is compounded annually, semiannually, or monthly?
b) One hundred dollars is to be received after one year. What is the present value of this amount if you can earn 12 percent compounded annually, semiannually, or monthly?
Explanation / Answer
Value of saving = $100
Annual Interest rate = 12%
Value of saving if compound annually
Value after one year = $100 × (1 + 12%)
= $112
Hence, value of saving if compound annually is $112.
Value of saving if compound Semiannually
Value after one year = $100 × (1 + 12%/2) ^2
= $112.36
Hence, value of saving if compound semiannually is $112.36
Value of saving if compound Quarterly
Value after one year = $100 × (1 + 12%/4) ^4
= $112.55
Hence, value of saving if compound quarterly is $112.55
Amount received after one year = $100
Present value if compound annually
Present value = $100 / (1 + 12%)
= $89.29
Hence, present value if compound annually is $89.29.
Present value if compound Semiannually
Present value = $100 / (1 + 12%/2) ^2
= $89
Hence, Present value if compound semiannually is $89
Present value if compound Quarterly
Present value = $100 × (1 + 12%/4) ^4
= $88.85
Hence, present value if compound quarterly is $88.85
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