Determine the balance A for P dollars invested at rate R compounded N times per year for T years. Round each amount to the nearest cent
P= $1000, R=3% t=10 years
N=A
2=?
4=?
12=?
365=?
Compounded continuously=?
A = Po(1+r)^c
r = 0.03/n = 0.03/2 = 0.015 = Semi-annual % rate.
c = 2Comp./yr. * 10yrs. = 20 Compounding periods(N*t).
A = 1000(1+0.015)^20 = $1346.86.
Repeat for the remaining values of N.
To determine the balance A for P dollars invested at rate R compounded N times per year for T years, we can use the compound interest formula:
A = P * (1 + R/N)^(N*T)
Given:
P = $1000
R = 3% = 0.03
T = 10
1. For N = 2:
A = 1000 * (1 + 0.03/2)^(2*10)
= 1000 * (1 + 0.015)^(20)
≈ $1343.92
2. For N = 4:
A = 1000 * (1 + 0.03/4)^(4*10)
= 1000 * (1 + 0.0075)^(40)
≈ $1360.48
3. For N = 12:
A = 1000 * (1 + 0.03/12)^(12*10)
= 1000 * (1 + 0.0025)^(120)
≈ $1377.21
4. For N = 365:
A = 1000 * (1 + 0.03/365)^(365*10)
= 1000 * (1 + 0.000082)^(3650)
≈ $1377.54
For compounded continuously, we can use the formula:
A = P * e^(R*T)
5. For compounded continuously:
A = 1000 * e^(0.03*10)
= 1000 * e^(0.3)
≈ $1349.86
Therefore, rounding each amount to the nearest cent:
1. For N = 2: A ≈ $1343.92
2. For N = 4: A ≈ $1360.48
3. For N = 12: A ≈ $1377.21
4. For N = 365: A ≈ $1377.54
Compounded continuously: A ≈ $1349.86