Explanation Given : Initial deposit in the account is $ 10 , 000 , and APR is 3.5 % and time for which money deposited is: (a)1 year, (b) 5 years, (c) 20 years. The formula to calculate final amount in continuous compounding is, F .V=I .V × e APR × t Where, ➣ F .V is final value after continuous compounding. ➣ I .V is initial value of principal amount. ➣ APR is annual percentage rate. ➣ t is time for which money remains invested. Calculation: (a) For t = 1 year The formula to calculate final amount in continuous compounding is, F .V=I .V × e APR × t Substitute $ 10 , 000 for I .V , 0.035 for APR , 1 for t . F .V = 10 , 000 × e 0.035 × 1 = 10 , 000 × 1.035619 = $ 10 , 356.197 (b) For t = 5 years The formula to calculate final amount in continuous compounding is, F .V=I .V × e APR × t Substitute $ 10 , 000 for I .V , 0.035 for APR , 5 for t . F .V = 10 , 000 × e 0.035 × 5 = 10 , 000 × 1.191246 = $ 11 , 912.462 (c) For t = 20 years The formula to calculate final amount in continuous compounding is, F .V=I .V × e APR × t Substitute $ 10 , 000 for I .V , 0.035 for APR , 20 for t . F .V = 10 , 000 × e 0.035 × 20 = 10 , 000 × 2.01375 = $ 20 , 137.527 The formula to calculate annual percentage yield for continuous compounding is, APY= [ 1 + r n ] n − 1 …… (I) Where, ➣ r is interest rate (APR) in decimal...

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Chapter 4.B, Problem 75E

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Annual percentage yield for continuous compounding and the final balance of an account with an initial deposit of $$ 10, 000$ , an APR of $3.5 %$ after $1$ , $5$ and $20 years$ .

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Chapter 4.B, Problem 74E

Chapter 4.B, Problem 76E

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Annual percentage yield for continuous compounding and the final balance of an account with an initial deposit of $ 10 , 000 , an APR of 3.5 % after 1 , 5 and 20 years .

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Annual percentage yield for continuous compounding and the final balance of an account with an initial deposit of $10,000 , an APR of 3.5% after 1 ,5 and 20 years .

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Annual percentage yield for continuous compounding and the final balance of an account with an initial deposit of $$ 10, 000$ , an APR of $3.5 %$ after $1$ , $5$ and $20 years$ .