Simple interest is the interest that is computed on the original principal only.
If I denotes the interest on a principal P (in dollars) at an interest rate of r per year for t years, then we have
I = Prt
The accumulated amount A, the sum of the principal and interest after t years is given by and is a linear function of t.
A= P + I = P + Prt = P(1 + rt)
A bank pays simple interest at the rate of 8% per year for certain deposits.
a. If a customer deposits $1000 and makes no withdrawals for 3 years, what is the total amount on deposit at the end of three years?
P = 1000, r = 0.08, and t = 3 A=P(I+rt)=1000[1+(0.08)(3)]=1240 or $1240
b. What is the interest earned in that ...view middle of the document...
Annually b. Semiannually c. Quarterly . Daily
Annually, where, P = 1000, r = 0.08, and m = 1. Thus, i = r = 0.08 and n = 3, so A=1000[1 + (0.08/1)]^3 = 1259.71
b. Semiannually, Here, P = 1000, r = 0.08, and m = 2. Thus, i=0.08/2 and n = (3)(2) = 6, so A=1000[1+(0.08/2)]^6 =1265.32
c. Quarterly. P = 1000, r = 0.08, and m = 4.Thus, i=0.08/4 and n = (3)(4) = 12, so A=1000[1+(0.08/4)]^12 = 1268.24
d. Daily. P = 1000, r = 0.08, and m = 365. Thus,i=0.08/365 and n = (3)(365) = 1095, so A=1000[1+(0.08/365)]^1095 = 1271.22
Continuous Compound Interest Formula
A = Pe^rt where P= Principal r = Annual interest rate compounded continuously t= Time in years A= Accumulated amount at the end of t years
Find the accumulated amount after 3 years if $1000 is invested at 8% per year compounded (a) daily, and (b) continuously.
P = 1000, r = 0.08, m = 365, and t = 3, we find P = 1000, r = 0.08, and t = 3, we find
A = Pe^rt = 1000e^(0.08)(3) ≈ 1271.25
Note that the two solutions are very close to each other.
Effective Rate of Interest Formula
r(eff) = [1+(r/m)]^m - 1 where reff = Effective rate of interest r= Nominal interest rate per year m= Number of conversion periods per year
Find the effective rate of interest corresponding to a nominal rate of 8% per year compounded a. Annually
Annually. Let r = 0.08 and m = 1. Then r(eff) = [1+(.08/1)]^1 - 1 =0.08 = 8%
If the effective rate of interest reff is known, then the accumulated amount after t years on an investment of P dollars can be more readily...