Find the best balance after investing $12,000 for a period of 7 years at two different interest earning types: simple interest at 5% and compound interest at 4.5%. Round the answer to two decimal places.(1 point) The best balance after investing $12,000 for a period of 7 years is $
Find the best balance after investing $12,000 for a period of 7 years at two different interest earning types: simple interest at 5% and compound interest at 4.5%. Round the answer to two decimal places.(1 point) The best balance after investing $12,000 for a period of 7 years is $
The formula for simple interest is Principal x Rate x Time.
For simple interest, the balance after 7 years can be calculated as:
Balance = 12,000 x (1 + 0.05 x 7)
= 12,000 x (1 + 0.35)
= 12,000 x 1.35
= $16,200.
The formula for compound interest is P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
For compound interest, the balance after 7 years can be calculated as:
Balance = 12,000 x (1 + 0.045/1)^(1 x 7)
= 12,000 x (1 + 0.045)^7
= 12,000 x (1.045)^7
= $16,583.63.
Comparing the two balances, the best balance after investing $12,000 for a period of 7 years is $16,583.63.
To calculate the best balance after investing $12,000 for 7 years at different interest rates and earning types, we need to compare the total accrued amount from both simple and compound interest.
For simple interest:
Balance = Principal x (1 + Rate x Time)
= $12,000 x (1 + 0.05 x 7)
= $12,000 x 1.35
= $16,200
For compound interest:
Balance = Principal x (1 + Rate/100)^Time
= $12,000 x (1 + 0.045)^7
= $12,000 x 1.347675
= $16,171.10
The best balance, rounded to two decimal places, after investing $12,000 for a period of 7 years is $16,171.10.
To find the best balance after investing $12,000 for a period of 7 years at two different interest earning types, we need to calculate the balance for both simple interest and compound interest and compare the results.
1. Simple Interest:
The formula for calculating simple interest is:
I = P * r * t
Where:
I = Interest
P = Principal (initial investment)
r = Interest rate
t = Time period
Substituting the given values, we have:
I = $12,000 * 0.05 * 7
I = $4,200
The total balance after 7 years with simple interest is calculated by adding the interest to the principal:
Balance = Principal + Interest
Balance = $12,000 + $4,200
Balance = $16,200
2. Compound Interest:
The formula for calculating compound interest is:
A = P * (1 + r/n)^(n*t)
Where:
A = Total balance (including interest)
P = Principal (initial investment)
r = Annual interest rate (expressed as a decimal)
n = Number of times interest is compounded per year
t = Time period in years
Substituting the given values, we have:
A = $12,000 * (1 + 0.045/1)^(1*7)
A = $12,000 * (1 + 0.045)^7
A = $12,000 * (1.045)^7
A = $15,762.058
Rounding the answer to two decimal places, we get:
Balance = $15,762.06
Therefore, the best balance after investing $12,000 for a period of 7 years is $15,762.06, with compound interest at 4.5%.