Interest- compounded continuously?

Question

If you invest $7,500.00 in an account paying 8.35% compounded continuously, how much money will be in the account at the end of

(A)5.5 years?
(B)12 years?

Best answer defines compounded continously, shows the problem step by step and solution. Explains well. Thanks in advance.

Answer 1

Pe^(rt) is the continously compounded formula.

P = Principal = 7500
e = mathematical constant (approx 2.718)
r= rate = 8.35%
t = A.)5.5 B.) 12

A.) 11,871.64
B.) 20,427.93

Answer 2

Principal (P) = 7500
rate (j) = 8.35 percent
m= 1 (annually)
i= j/m = 8.35/1 = 8.35 percent

A. time= 5.5years
n= mt =1(5.5) =5.5

S=P(1+i)^n
=7500 (1+8.35percent)^5.5
=7500 (1.554386573)
=$11657.90

B. time (t) = 12
n= mt = 1(12) =12

S=P(1+i)^n
=7500(1+8.35percent)^12
=7500 (2.617863439)
=$19633.98


j is the nominal rate. Nominal rate is a quoted rate in a compound m is the no. of conversion period per year
conversion period: no. of conversion period:
quarterly 4
semi-annually 2
annually 1
monthly 12

i is the rate per interest period.. i = j/m