Reba is comparing two types of savings accounts.

Question

Reba is comparing two types of savings accounts. Account A has a 6% annual simple interest rate, while Account C has a 5% annual interest rate compounded yearly. For an initial investment of $200, Reba calculates that in four years, Account A will have $248 and Account C will have $243.10. She concludes that Account A is the better choice. Is she correct? Explain.

The better choice depends on the {select choice Length of the investment, Interest rate, Initial amount invested}. Because the {select choice Simple, Compound} interest account has a greater annual interest rate, it initially has a greater yield. However, after year {select choice 8, 4, 2} the {select choice Compound, Simple} interest investment will be the better choice.

Answer 1

Answer 2

in the normal world, 6% simple interest is the same as 6% compounded yearly

for P=200, after four years the amount in the account=200*1.06⁴=252.50

Agree 5% yearly interest on 200 after 4 years is amount=200*1.05⁴=243.10

6% yearly (simple) interest better than 5% yearly compounded any amount of time

in the normal world.

The problem I guess is imagining after each year for the 6% account, $12. is taken out and put into

a zero interest account, so the interest account each year only makes $12..

then question is, when is 200+12x<200*1.05^x

at x=8 (end of eight years)

the dumb 6% account has $296 while the normal 5% account has $295.49

It is when x=9 the dumb 6% account is no longer better,,,,308<310.27

Answer 3

Hello Elo,

Initial investment and interest rates are held constant for this problem. Initial investment is $200, interest rates are 6% on account A and 5% on account B. The only thing that changes is length of investment, so the better choice depends on length of investment.

Now, to the second question, we know that Account A, the Simple Interest account, still exceeds Account B at year 4 ($248 vs. $243.10). Simple interest has greater initial yield. That means simple interest will also be higher at year 2, so we need to check year 8.

Account A at Year 8:

A=P(1+rt)

A=200(1+0.06*8) = $296

Account B at Year 8:

A=P(1 + r/n)^nt

n=1 here, since we compound annually

A=200(1 + 0.05/1)^1*8

A=$295.49

This is very close, so your next step would be to compute both simple and compound interest at year 9. I'll leave the specific computations to you--just substitute 9 in for t--but you will find that compound interest overtakes simple at this point, so compound interest and account B will be the better choice after year 8.

I hope this helps.