How did they arrive at this answer ?

Question

Tanya's uncle Joe said he would give her so money so she could open a savings account. He gave her $5000.00. She opened an account with 3% interest. How much interest had the account earned after the first 6 months? Answer is 7.50 (no problem there)
Here is where I couldnt figure out.

If Tanya did not make any withdrawals, how much money was in her account at the end of the first eight months? The answer given is $ 1050.00 ( I couldnt figure how that answer came to be and there were some typo's in this booklet)

Answer 1

$5000 to open the account

At 3% interest, the account would accrue $150 dollars interest monthly, and after six months this would be $900 (not $750 because you're forgetting month one).

So at the end of eight months (adding $150 twice more), Tanya has $6200 in her savings account.

Interest = Principal X Rate X Time

Interest = $5000 X 3% X .5 years = $75

I don't see how the book writers got that answer either, but transposed answers in the back of the book are not uncommon.

Have a great day!

Answer 2

Clearly, her identity was stolen after she gave out her bank information in response to a bogus email and someone almost cleaned out her bank account. For some reason, the thief had a little bit of a conscience and he left Tanya with some of her money.

Or it's a typo.

There is a problem with the first answer as well.

Even if this is simple interest (interest paid only on the principal, not on the accumulated interest), after 6 months she should have $75 in interest, or a total of $5075. After 8 months, she should have $100 in interest, or a total of $5100.

Usually interest is compounded monthly on savings accounts. The amount of interest applied each month would be 1/12 of 3% or in decimals .0025 of however much was in the account for that month. The first month, she would earn $12.50 based on $5000. The second month, she would earn $12.53 because there was not $5012.50 in the account for that month. The third month, she would earn $12.56, and so forth.

The amount of money in the bank after M months of compounded interest would be 5000*(1.0025)^M.

Based on this formula, after 6 months she would have $5075.47, meaning she had earned $75.47. After 8 months she would have about $5100.88, meaning she had earned $100.88. Compounding the interest would mean at the end of the year, she would have $5152.08, which is a little over $2 more than she would have if the interest were not compounded.

I hope that is not too much information, but I wanted you to understand how interest really works.

PS There are a wide range of bizarre answers above. Interest rates are usually quoted as annual rates, so the bank account would not be paid 3% per month. (I'd love to have that kind of bank account, which would be paying 36% per year!) I know what I am doing, so please trust me. I teach advanced math and calculus as well as working as the business manager of a private school.

Answer 3

Next time you ask a question like this. Try to include information such as the rate of compounding. I think I know where you're going with this question. In 6 months the interest earned is $75= 5000(r)=5000*.03 So for 8 months, take (75/6)*8. Or another way is to say well in a year without withdrawls this will earn 5000*.03 in interest. 8 months is 2/3 of one year. Hence, (2/3)*150=100

Answer 4

The money in the account, with no withdrawals, must be the principal plus the interest. So the correct answer is $5100.00 if you are computing simple and not compound interest.

(FYI 1.5 % of 5000 = 75, not 7.5)

Simple interest = 5000 x 3/4 or .75 year (8 months) x .03 (3%)
Compund interest = 5000 x 1/12 x .03 for the first month, then multiply that by 1/12 x .03 for the second month, etc.
[Anyone multiplying by 8 is wrong, that would imply 8 years. 8 months is 3/4 of a year.]

I=PRT or Interest = Principal * Rate (interest %) * Time (length)

Answer 5

Whao. Typos galore in that booklet.

If you need to know how much a compound interest yields, you take 1 + (interest rate in absolute value) and raise that to the power of the number of years.

In this case we have 1 + 0.03, and for six month, raise 1.03 to the power of 0.5 (half a year) yielding a (current value)/(initial value) ratio of 1.015 (1.014889 but we'll skip all the extra decimals).

1.015 times $5000 is 5075, so the interest is $75, so either the $7.50 is wrong or the initial $5000 should have been $500.

For eight month, you raise 1.03 to the power of 0.66666 (as eight month is 2/3 of the year), that gives 1.0199 -- we'll use 1.02 for shorts, and 1.02 times $5000 is $5100, so $100 in interest.

If this is the kind of accounting that bank is doing, may I suggest you take your money elsewhere? They don't seem too good with numbers.

Answer 6

In 6 months, $75 is earned (not 7.50). At 8 months, there would be $100 interest which puts the balance at $5100. This of course is assuming simple interest throughout.

By the way, caffeinated is doing 8 years not 8 months

Answer 7

Using the compound interest formula
M = $5000.00 (1 + .03)^8 = $11350.00
$1050.00 is from typo land.

Answer 8

i agree with the person that said its 6200

Interest= p*r*t

so she started with a premium of 5,000 at 3% for 8 months

if you multiply that out as 5,000*.03*8 the answer is 1200. That however is only the interest she earned. If she didnt make any withdrawals, she has the initial 5,000 plus the interest she earned because she didnt make any withdrawals, so the answer is 6200

Answer 9

I have to agree with just wondering. I'd *love* to be getting 142.576% annual. The formula for compounding intererst is
V = (1+r)ⁿ * P
where V is total value, P is the principle (original) value, r is the rate (expressed as a decimal. 3% = .03), and n is the number of periods the interest has compounded.

Actually........ It'd be kewl just to have an Uncle Joe like hers


Doug

Answer 10

She earns simple interest of $12.50 per month. In 6 months she earns $75 in interest and in 8 months she earns $100. So the answer should be $5100.