# Further math question....

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#1
Context/unit: Sequences and series: Using standard results

Ok, the full question is
You have \$20 000 to invest for one year. You put it in the following bank account:
'Flexible Saver': 1.5% interest APR (annual percentage rate)
-> Interest calculated monthly (i.e 1.5/12% of balance each month)
-> Interest paid annually, into a seperate account
-> No limits on withdrawals or balance
Your bank then informs you of a new savings account, which you are allowed to open as well as the Flexible Saver.
'Regular Saver': 5% interest APR
-> Interest calculated monthly
-> Interest paid anually, into a seperate account
-> Maximum \$1000 balance increase per month

Assuming you initially have your money in the Flexible Saver, but transfer as much as you can into a Regular Saver each month, calculate how much extra money you will earn compared to what would happen if you just left it in the Flexible Saver all year.

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Okay, so I don't really understand the question. Do you transfer money from the Flexible Saver account to the Regular Saver account each month? But this wouldnt make sense since the interest is paid annually, so you'll have to use the 20 000. Also, when you calculate the interest each month, would you also include the additional money earned each month? This wouldn't also make sense since, again, the interest is paid anually. I don't get it. Can someone help? In the mark scheme, the answer is \$227.50. I know compound interest rates can be calculated with a(1+n%)^n but this question is about series, not exponents. I'm confused, need help!
Last edited by adanjargon; 1 year ago
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#2
Here's a screenshot of the actual question:
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1 year ago
#3
Is the intention that compound interest isn’t used - so the interest paid is just on the balance at the end of the month.

So if the money was left in flexible saver:

I = 20000 * 1.5 * 12 / 12 / 100 = 300

Then if you transfer 1000 / month

Flex I = Sigma 1-12 (19000 -1000n)1.5/1200 = 202.5

Reg I = Sigma 1-12 (1000 + 1000n)5/1200 = 325

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