find (a) the compound amount and (b) the compound interest for the given investment and annual rate.
a. $5000 for 20 years at 5% compounded annually
b. $700 for 15 years at 7% compounded semiannually.
To find the compound amount and compound interest for these investments, you can use the compound interest formula:
Compound Amount = Principal (1 + interest rate/number of periods)^(number of periods * number of years)
Compound Interest = Compound Amount - Principal
Let's calculate the answers for each scenario:
a. $5000 for 20 years at 5% compounded annually:
Principal (P) = $5000
Annual Interest Rate (r) = 5% = 0.05
Number of Periods/Compounding Frequency (n) = 1 (compounded annually)
Number of Years (t) = 20
Using the formula:
Compound Amount = $5000 (1 + 0.05/1)^(1 * 20) = $5000 (1 + 0.05)^20 ≈ $12,578.22
Compound Interest = $12,578.22 - $5000 ≈ $7578.22
Therefore, the compound amount is approximately $12,578.22, and the compound interest is approximately $7578.22.
b. $700 for 15 years at 7% compounded semiannually:
Principal (P) = $700
Annual Interest Rate (r) = 7% = 0.07
Number of Periods/Compounding Frequency (n) = 2 (compounded semiannually)
Number of Years (t) = 15
Using the formula:
Compound Amount = $700 (1 + 0.07/2)^(2 * 15) ≈ $700 (1 + 0.035)^30 ≈ $1962.38
Compound Interest = $1962.38 - $700 ≈ $1262.38
Therefore, the compound amount is approximately $1962.38, and the compound interest is approximately $1262.38.