题目
A client invests €20,000 in a four-year certificate of deposit (CD) that annually pays interest of 3.5%. The annual CD interest payments are automatically reinvested in a separate savings account at a stated annual interest rate of 2% compounded monthly. At maturity, the value of the combined asset is closest to:
选项
A.€21,670.
B.€22,890.
C.€22,950.
答案
B
解析
B is correct, as the following cash flows show:「huixue_img/importSubject/1564548693586219008.png」The first payment grows at 2.0% compounded monthly for three years (where FV is future value):「huixue_img/importSubject/1564548693657522176.png」The second payment grows at 2.0% compounded monthly for two years:「huixue_img/importSubject/1564548693724631040.png」The third payment grows at 2.0% compounded monthly for one year:「huixue_img/importSubject/1564548693795934208.png」The fourth payment is paid at the end of Year 4. Its future value is €700. The sum of all future value payments is as follows:「huixue_img/importSubject/1564548693867237376.png」 B正确。 方法一：如下现金流所示 这四笔年利率是根据存单3.5%的年利率计算的：€20,000*3.5%=€7,000。 第一笔利息€7,000以2.0%名义年率按照每月复利计息，为期三年(其中FV为未来价值): FV=€700(1＋0.02/12)^(3×12)=743.25 第二笔利息€7,000以2.0%名义年率按照每月复利计息，为期两年: FV=€700(1＋0.02/12)^(2×12)= 728.54 第三笔利息€7,000以2.0%名义年率按照每月复利计息，为期一年: FV=€700(1＋0.02/12)^(3×12)=714.13 第四笔利息€7,000在第4年年底支付。它的未来价值就是€700。 所有未来价值支付的总和如下: €20,000.00＋€743.25＋€728.54＋€714.13＋€700.00=€22,885.92 Or 方法二: 1＋EAR (with a stated annual interest rate of 2.0% compounded monthly)=(1＋0.02/12)^12=1.02018436 END model： PV=0, PMT=700, I/Y=2.018436, N=4, CPT FV=2,885.92. Total Future value is €22,885.925=€2,885.925 €20,000.