Unless you are willing to invest for 27 years

Question

Unless you are willing to invest for 27 years or more, 5% compound interest will not beat 10% simple interest. Is it true or falso?

(Note: i cannot understand well that question, if you can give me a short explain I will be gratefully)

Answer 1

With 10% simple interest, you gain 10% of your original investment every year.

So, if your initial amount is P, then at the end of each year you will have

10% of your original investment added (that's the same amount of dollars

added each year.

Year Amount

1 P + 0.10P

2 P + 0.10P + 0.10P = P + 2(0.10)P

3 P + 0.10P + 0.10P + 0.10P = P + 3(0.10)P

N P + NP(0.10)

With 5% compound interest, at the end of each year you will have increased

by 5% OF THE PREVIOUS YEAR's amount.

Year Amount

1 P + 0.05P = 1.05P

2 1.05 times the amount you had at the end of year 1, which was 1.05P,

so you have 1.05(1.05)P = (1.05)^2)P (1.05)^2 is 1.05 squared

3 1.05 times the amount you had at the end of year 2, which was (1.05)^P,

so you have (1.05)^3)P

N (1.05)^NP

So say P=1 dollar.

At year N, 10% simple interest you will have 1+N(0.10),

while with 5% compound interest you will have (1.05)^N dollars.

By 27 years, the (1.05)^N will finally exceed the 1+N(0.10).

At N=27, (1.05)^27 = 3.733 while 1+ 27(0.10)= 3.700

Answer 2

invest C

after n years

5 % compound , C ( 1 + 0.05)ⁿ

10 % simple, C + 0.10 Cn

So C (1 + 0.05) ⁿ > C + 0.10Cn when n>= 27