Problem

Savings Plans On January 1, Kim places $\$ 1000$ …

05:02

Problem 49 Hard Difficulty

Jim places $\$ 1000$ in a bank account that pays $5.6 \%$ compounded continuously. After 1 year, will he have enough money to buy a computer system that costs $\$ 1060 ?$ If another bank will pay Jim $5.9 \%$ compounded monthly, is this a better deal?

Answer

Not quite. Jim will have $1057.60. The second bank gives a better deal, since Jim will have
$1060.62 after 1 yr.

Related Courses

Algebra

Precalculus

Chapter 5

Exponential and Logarithmic Functions

Section 7

Financial Models

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Video Transcript

and this question, given that the principle is that $1000 on that the rate of interest is equal to 5.6% should the same as your friends you five six. Also, given that time is a year, one year that's compounded continues. Comfort continue. So we know that if you use this formula raised a lot after two years, so the first step is going to be to plug all of this information. Did you pay into the equation both and so free a physical 2000 times E to the power off our 56? It's one. Now if you just plug all of this too calculator, get 57.6. That's a dollars. But the question is asking us if after one year we'll have enough money to buy a computer system that costs about 60. Since this value is less $1060 the answer is enough. He though now the second part of this question saying is asking that if another banquet page in 59% compounded monthly, is this a better deal? So to solve this used de compounded interest formula, okay, P one plus are over and power and cheese. A is the amount of 50 years, Um, and he's a principal and is a number number compounds far is a rate of interest on T is the number of years enter. First we're gonna do is write down all the information that we're given. So given that the rate is five point 9% 5.9% Gee, Galtier's your guns your five night were also given. That's competent month, these 12 and the principal. It's also $1000. But all of this information to formula you get a Is he going to 1000? One plus are 59 12 to the power 12 times T, which is also one year now. If you plug all of this into get values off, that does 60 26 2 on this is greater than 1016 60 and therefore, yes, that is a better deal. Continuing now beautiful to afforded the computer

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