Question

Jim places ​$10,000 in a bank account that pays 9.8​% compounded continuously. After 2 ​years, will he have enough money to buy a car that costs ​$12 comma 160​? If another bank will pay Jim 10​% compounded semiannually​, is this a better​ deal?

Answer 1

Answer:

9.8% compounded continuously is a better deal

Step-by-step explanation:

Given that Jim wants to buy a car which costs 12160 after 2 years.

He has two options before him,

i) 9.8% compounded continuously

ii) 10% compounded semiannually

Principal he has is 10000 dollars

Hence we have

Value after 2 years for option i) = $10000e^{0.098(2)} \\=12165.27$

(after rounding off to two decimals)

Option ii)

For compounding continuously for 4 half years we get

Final amount = $10000(1+\frac{10}{200} )^{4} \\=10000(1.05)^4\\= 12155.06$

(after rounding off to two decimals)

Comparing we find sufficient cash is provided by option I