Question

1. find the balance after one year if you deposit all the money into an account that pays $2.50 in simple interest each month (this is a simple equation where the amount of interest stays the same each month).

2. Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding. ​

Answer 1

1. Balance after 1 year with simple interest= 600 + (2.5 x 12) = 600 + 30 = $630

2. Balance after 1 year with compounded interest = P ( 1 + $\frac{r}{n}$$)^{nt}$

= 600 ( 1 + $\frac{0.05}{12}$$)^{12}$= 600 (1.0511) = $630.66 = approx. $630

Answer 2

If $600 is deposited into an account that pays $2.50 per month, the total amount after a year will be $630. If you instead deposited into an account earning 5%, the amount would be $630.70.

If you earn $2.50 per month, in a year you will earn:

= 2.50 x 12 months

= $30

Added to the original $600:

= 600 + 30

= $630

If the account makes 5% and is compounded monthly, you need to convert this rate to a monthly rate as well as the time period:

5% = 5/12 = 5/12% per month

1 year = 1 x 12 = 12 months

The amount after a year will be:

= Amount x ( 1 + rate) ^ number of periods

= 600 x ( 1 + 5/12%)¹²

= $630.70

In conclusion, you will have $630 using simple interest and $630.70 using monthly compounding.

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