Question

Jim places $10,000 in a bank account that pays 11.6% compounded continuously. After 2 years, will he have enough money to buy a car that costs $12,618? If another bank will pay Jim 12% compounded semiannually, is this a better deal? After 2 years, Jim will have $ (Round to the nearest cent as needed.) Jim will have enough money to buy the $12,618 car after 2 years. After 2 years, the other bank will yield $ (Round to the nearest cent as needed.) Is the other bank's offer better deal? No. Jim's bank (11.6% compounded continuously) is better. O Yes. The other bank (12% compounded semiannually) is better.

Answer 1

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A We have the When A = Amount continuous compounding formula, Ac pent oftur time a P = Principal amount = $10000 for state of interest (in decimal) = 0.116 Now, when to2 then we have, # Now we have nt As $210000 x 2 (0-16x)} = $ 210000 x 60-239] ~ $112611.201 compound Extinest formula, A =P ( 1+ 22 h where p= $10000, 70=0.12, n. 2, So, here $21 9000 x (14 0:42) 243} ${ x (1.05)9} * 12624.77 ta A = 10000 x

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So we have,

After 2 years, Jim will have $12611.20​​​​​​

Jim will not have enough money to buy the $12,618 car after 2 years.

After 2 years, the other bank will yield $12624.77​​​​​​

Yes, The other bank (12% compounded semi annually) is better.