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

9.8% compounded continuously is a better deal

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+(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