Question

Brandon invested $9,200 in an account paying an interest rate of 3 1/4%

compunded quarterly. Lamonte invested $9,200 in an account paying an interest rate of 2 7/8% compounded monthly. After 19 years, how much more money would Brandon have in his account than Lamonte, to the nearest dollar?

Answer 1

$1141

Explanation:

The general formula for compound interest is:

`A(t)=P(1+r/n)^n^t`, where A is the amount in dollars, P is the principal (i.e., amount invested), r is the interest rate, n is the number of compounding periods, and t is the time in years.

For Brandon's account (and equation), P = $9200, r = 0.0325, n = 4 and t = 19.

Explanations for r and n:

• We always convert the percentage to a decimal when dealing with interest. 3 1/4% is the same as 3.25%. We find the decimal by moving the decimal point two places to the right or by dividing 3.25 by 100 which gives us r = 0.0325
• Quarterly divides a unit into 4. There are 12 months in a year and dividing 12 into 4 means that the money is compounded every 3 months

Now, we can simply plug in everything to find the amount Brandon would have in 19 years and round to the nearest dollar (i.e., nearest whole number):

`A_(Brandon)(19)=9200(1+0.0325/4)^(^4^*^1^9^)\\ A_(Brandon)(19)=9200(1.008125)^7^6\\ A_(Brandon(19))=17016.92431=17017`

For Lamonte's account (and equation), P = $9200, r = 0.02875, n = 12, and t = 19

Explanations for r and n:

• 2 7/8% is the same as 2.875% and when we move the decimal two places to the left (or divide 2.875 by 100), our decimal for r is 0.02875

• There are 12 months in year so monthly means that the money is compounded every month. This is why n = 12 when money is compounded monthly

We can again plug in the values into the general equation to find the amount Lamonte would have in 19 years and round to the nearest dollar/whole number:

`A_(Lamonte)(19)=9200(1+0.02875/12)^(^1^2^*^1^9^)\\ A_(Lamonte)(19)=9200(1.002395833)^2^2^8\\A_(Lamonte)(19)=15875.86592=15876`

Now we can subtract Lamonte's amount (15875) from Brandon's (17017) to find how much more Brandon would have in his account than Lamonte in 19 years:

17017 - 15876 = $1141

**If you didn't do any intermediate rounding and waited until the very last subtraction to round, you'd still get a similar answer

17016.92431 - 15875.86713 = 1141.05718 = $1141