a) $$ 131.44$b) 906.44 dollarsc) $$ 32.86$d) answer no availablee) $$ 32.86$f) $$ 807.86$g) $$ 34.25$h) Both earn very same interest because that the 2nd year.q




You are watching: Ryan deposits $775 in an account


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Video Transcript

okay, in this problem, we have Ryan and we have actually Brian, Ryan and Brian both deposit $775 apiece. Lock both get an interest price of 4.24%. Basic interest. One of them is collected after 4 years, and also the other is ~ one year. Therefore let's work on Ryan. What is his attention after the 4 years? So we take his principal 7 75 main point it by his interest rate, converted to a decimal 750.4 come 4 and multiply the by 4 years. That tells united state the amount of money the made an interest in the 4 year period is $131.44. Therefore let's uncover his balance. At the finish of the 4 years, we're walking to add his interest and his major together, 7 75 add to 1 31 44 offers us his balance the $906.44. Okay, just how much interested right here in the very first year? Well, what we deserve to do is we can take the lot of attention he earn altogether and divided by four. And also that will tell us the amount of interest each year. So when we divide that by four, we check out that he earned $32.86 the very first year. So how much interested he earned in the 4th year? The very same thing. The earned the same amount the interest annually for 4 years. It was all provided to him in ~ the end of the 4 year duration in one chunk. Currently we're going to rotate our attention to Brian. What is Brian's attention after the an initial year? So us take Brian's ethics 7 75 times his interest as a decimal 0.4 to 4 times one for one year, and also we get $32.86. Therefore Brian earn the very same amount of interest throughout your one as Ryan. What is Brian's balance after the very first year? Let's include that money to his initial 7 75 and we acquire $807.86. Okay, currently what Brian's walking to do is he's going to take that chunk that money he currently has. He's going to reinvest it, and we're gonna discover his interest for a year to, therefore we're gonna take $807.86. Invest at 4.24% 0.4 to 4 is the decimal because that one year. And let's see what he has now. That earned $34 in 25 cent interest in that 2nd year. Now notice that the is higher than what that earned the very first year because he has actually earned interest on his interest. So following we're walking to compare his attention from year to $34.25 with Ryan's interest from year to. And remember, Ryan's attention was the very same every year. For this reason Ryan obtained $32.86 every year. That got much more clearly, Brian gained more. Why did try and get more interest? together I claimed a minute ago, that got an ext interest since he was earning interest on his interest. The re deposit the attention earned from your one and he earn attention on that. And also that's what we speak to calm, pounding