Ethan has a sum of money that he wants to invest. He is comparing savings accounts at different banks. Bank A offers an interest rate of three percent. After one year of investing with bank A, Ethan’s investment will have a value of 1442 pounds. Bank B offers an interest rate of four percent. How much will Ethan’s investment be worth after one year of investing with bank B?
So to solve this problem, the first thing we want to do is work out how much Ethan’s initial investment was. And to do that, we can use the information about bank A.
If we call Ethan’s initial investment 𝐼, then what we’re gonna do is use the information we’ve got about bank A. So we know that it’s got an interest rate of three percent. And we know that after one year of banking with bank A, Ethan’s investment will have a value of 1442 pounds, to find out what his initial investment was.
There’s a couple of methods we could use here and I’m gonna show you both. And this is called reverse percentage because we’re actually having an amount. And then we’re gonna to work backwards to find the original amount.
So what we can say is that 1442 pounds is gonna be equal to the initial investment then multiplied by and we’ve got one plus three over 100. And that’s because one would mean the initial investment itself then plus three percent would be three over 100 because percent means out of 100. So three out of 100 would give us that three over 100.
So therefore, what we have is that 1442 is equal to 𝐼 multiplied by 1.03, with 1.03 being our multiplier. And we got 1.03 because three over 100 is the same as 0.03. So therefore, what we want to do is divide each side of the equation by 1.03 to find 𝐼.
So we can say that 1442 over 1.03 is equal to 𝐼. So 𝐼 the initial investment is equal to 1400 pounds.
Now I said that I was gonna show you another way that you could work this out. And I’m gonna do that now. It is not that dissimilar; it just sets out in a slightly different way.
So if we consider the original investment, well the original investment would have to be multiplied by 1.03 to get to 1442. And the reason we know that it’s 1.03 that we multiplied by is cause we think of the original as 100 percent. Then, we’re gonna add three percent cause it’s an interest rate of three percent. And it’s just one year. So that means we’re gonna have 103 percent.
Now, 103 percent is the same as 103 over 100 which would be equal to 1.03. Okay, so that showed us how we get our multiplier. Now, let’s get back to the example that we’re showing.
So to get from the initial amount, you have to multiply by 1.03 to get to 1442. So therefore, to get from 1442 back to the initial amount, we’re gonna have to do the inverse which is divide by 1.03.
So then, we arrive at the same point we did with the original method. And that’s 𝐼 is equal to 1442 over 1.03 which gives us 1400 pounds.
Okay, so now we’ve found out what is the original investment was. What we need to do is find out how much will Ethan’s investment be worth after one year of investing with bank B.
Well, if we take a look at bank B, well bank B has an interest rate of four percent. So therefore, we can say that after one year at bank B, the amount in the account is going to be equal to the initial investment which is 1442 pounds multiplied by one plus four over 100 and that’s cause that’s four percent, which is gonna be equal to 1400 multiplied by 1.04.
So therefore, we can say that Ethan’s investment will be worth after one year of investing with bank B 1456 pounds.