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Chapter 4: 4-9-26BP (page 283)

Question: Determine the amount of money in a savings account at the end of 10 years, given an initial deposit of $5,500 and a 12 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.

Short Answer

Expert verified

Answer

The future value in the savings account in case of annual, semi-annual and quarterly compounding is $17,082.17, $17,639.25 and $17,941.21, respectively.

Step by step solution

01

Identification of the required information

Present value (PV) = $5,500

Periods for annual compounding (n1) = 10

Interest Rate for annual compounding (i1) = 12%

Periods for semiannual compounding (n2) = 20 (10*2)

Interest Rate for semiannual compounding (i2) = 12%

Periods for quarterly compounding (n3) = 20 (10*2)

Interest Rate for quarterly compounding (i3) = 3% (12%/4)

02

Future value of savings account (FV) in case of annual compounding

贵痴=笔痴脳(1+i)n=$5500脳(1+12%)10=$17,082.17

03

Future value of savings account (FV) in case of semiannual compounding

贵痴=笔痴脳(1+i)n2=$5500脳(1+6%)20=$17,639.25

04

Future value of savings account (FV) in case of quarterly compounding

贵痴=笔痴脳(1+i3)n3=$5500脳(1+3%)40=$17,941.21

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