Question

The National Bank of Wynona offers two types of savings account. The Top-Up-N-Saver account pays 2.5% annual compound interest, whereas the Super-Saver account pays 3% annual simple interest. If we put in $1,000 now and leave the money in the bank account for 10 years, which account would pay the most interest (and how much more)?

Select one:

a. The Top-Up-N-Saver account would pay $19.92 more in interest.

b. The Top-Up-N-Saver account would pay $50 more in interest.

c. The Super-Saver account would pay $50 more in interest.

d. The Super-Saver account would pay $19.92 more in interest.

e. Both accounts would pay the same interest.

Answer 1

Compound interest formula:

Amount = Principal * (1 + r)ⁿ

where, Amount is the value after 10 years, Principal = $1000, r= rate of interest = 2.5% and n is the tome period = 10

Now, putting these values in the above formula, we get,

Amount = $1000 * (1 + 2.5%)¹⁰

Amount = $1000 * (1 + 0.025)¹⁰

Amount = $1000 * 1.28

Amount = $1280.08

Interest = Amount - Principal invested

Interest = $1280.08 - $1000 = $280.08

Simple interest formula:

Interest = Principal * rate * time

where, Principal = $1000, r= rate of interest = 3% and n is the tome period = 10

Now, putting these values in the above formula, we get,

Interest = $1000 * 3% * 10

Interest = $10000 * 3%

Interest = $300

Interest under compound interest is $280.08 while under simple interest, it is $300. So, under simple interest, the accounts pays more interest.

Difference in interest = Simple interest - Compound interest

Difference in interest = $300 - $280.08 = $19.92