Find the missing final amount (future value) and interest earned.
Principal
Rate
Compounded
Time
Final
Amount
Compound
Interest
$7600
5
1
2%
annually
27 years
_____
_____
To find the missing final amount, we can use the formula:
Final Amount = Principal * (1 + (Rate/Compounded) )^(Compounded * Time)
Using the given values:
Principal = $7600
Rate = 2%
Compounded = 1 (annually)
Time = 27 years
Final Amount = 7600 * (1 + (0.02/1) )^(1 * 27)
Calculating this:
Final Amount ≈ $13,429.27
To find the interest earned, we can subtract the principal from the final amount:
Interest = Final Amount - Principal
Calculating this:
Interest ≈ $6,829.27
Therefore, the missing final amount is approximately $13,429.27 and the interest earned is approximately $6,829.27.
To find the missing final amount and compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final Amount
P = Principal
r = Annual Interest Rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
Principal (P) = $7600
Rate (r) = 2% = 0.02
Compounded (n) = 1 (annually)
Time (t) = 27 years
Let's calculate the missing values step by step:
1. Calculate the final amount (A):
A = $7600(1 + 0.02/1)^(1*27)
A ≈ $7600(1.02)^27
A ≈ $7600(1.8597)
A ≈ $14123.32
The missing final amount is approximately $14123.32.
2. Calculate the compound interest earned (CI):
CI = A - P
CI ≈ $14123.32 - $7600
CI ≈ $6523.32
The missing compound interest earned is approximately $6523.32.
Therefore, the missing values are:
Missing Final Amount = $14123.32
Compound Interest = $6523.32
To find the missing final amount and compound interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (future value)
P = Principal
r = Annual interest rate (in decimal form)
n = Number of times interest is compounded per year
t = Time in years
Using the given information, we can plug in the values and solve for the missing amounts.
1. Find the final amount (A):
A = 7600(1 + 0.02/1)^(1*27)
= 7600(1 + 0.02)^27
= 7600(1.02)^27
≈ 15,336.66
Therefore, the missing final amount is approximately $15,336.66.
2. Find the compound interest (I):
I = A - P
I = 15,336.66 - 7600
≈ 7736.66
Therefore, the missing compound interest is approximately $7,736.66.