Interest Question

Lex Luthor

Stumped on this one...any help appreciated

Person deposits €200 at the end of each quarter in their savings account
Money earns 5.5% AER

How much will the investment be at the end of 4 years?

I thought using the formula for a geometric series

a(1-r^n) ^n means to the power of n

---

1-r

where a =1.01375
r = 1.01375

I derived the 0.01375 as a quarter of 5.5% as paid in each quarter

Multiplied final answer by 200 but answer is wrong compared to answer sheet

Any guidance please to help me

Thanks

MathsManiac

Not sure how far out your answer was, but you seem to be missing a digit in your value for r. the fourth root of 1.055 is 1.013475...
(you're missing the 4.)
Does this account for the discrepancy between your answer and that in the provided solution?

MathsManiac

Sorry - just realised what you did wrong. It wasn't an omitted digit, but an incorrect calculation. You used a quarter of 5.5% as the quarterly interest rate. If interest is calculated and added quarterly, then the AER will NOT be four times the quarterly rate. Just as an annual rate of 5.5% is equivalent to annually multiplying the principal by 1.055, so too a quarterly interest rate of 1.375% is equivalent to multiplying the principal by 1.01375 every quarter. The effect of doing this is to multiply the principal annually by (1.01375)(1.01375)(1.01375)(1.01375), which is not 1.055. What you need to do to get the quarterly interest rate that yields an AER of 5.5% is to figure out: "What number do I need to multiply by every quarter in order to have the same effect as multiplying annually by 1.055?" The answer to this is the fourth root of 1.055.

That should get you back on track.

Yakuza

Just to add to MM's work, "n" will now be 16 as you're working in quarters, not years.
Find r', the new rate such that r'^4 = 1.055.
Then use your equation, but n is now 16.