Tyson and Ariana each invested $2,500 in separate accounts. Tyson’s interest rate is 5.75% and is compounded annually. Ariana’s simple interest rate is 5.75%. Neither will make any additional deposits or withdrawals. At the end of 6 years, how much more has Tyson earned? Round your answer to the nearest cent.
I don't know what to do here, please help. Please show me how to work it out.
Thanks!
Tyson
2500 * 1.0575^6 = 2500 * 1.39856 = 3496.41
Ariana
2500 * .0575 = 143.75 interest per year
143.75 * 6 = 862.50 interest total
+ 2500 = 3362.50
so 3496.41 - 3362.50
Thanks a bunch, please and Damon! You guys helped a lot.
Simple interest is calculated only on the amount of deposit, while compounding interest is calculated on principal, plus interest.
This is the difference between the 2 interest rate but they both have the same percentage.
pipi nut lol
To calculate the total amount earned by each person at the end of 6 years, we need to use the compound interest formula for Tyson and the simple interest formula for Ariana.
For Tyson:
The compound interest formula is: A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $2,500
r = 5.75% = 0.0575 (as a decimal)
n = 1 (compounded annually)
t = 6 years
Plug the values into the formula:
A = 2500(1 + 0.0575/1)^(1*6)
Calculate the value inside the parentheses:
A = 2500(1.0575)^6
Now, calculate the exponent:
A ≈ 2500(1.3699)
Finally, calculate the total amount earned by Tyson:
A ≈ $3,424.75
For Ariana:
The simple interest formula is: A = P(1 + rt)
Where:
A = the final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
t = number of years
In this case:
P = $2,500
r = 5.75% = 0.0575 (as a decimal)
t = 6 years
Plug the values into the formula:
A = 2500(1 + 0.0575*6)
Calculate the value inside the parentheses:
A = 2500(1 + 0.345)
Now, calculate the total amount earned by Ariana:
A ≈ $3,612.50
To find out how much more Tyson earned, subtract the amount earned by Ariana from the amount earned by Tyson:
$3,424.75 - $3,612.50 ≈ -$187.75
So, Tyson earned approximately $187.75 less than Ariana at the end of 6 years.