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Continuous Interest
The basis for continuous compound interest. See the following example to know the basis for continuous interest.
Example 1.
Suppose $1,000 is deposited in a savings account that earns compounded interest at a rate of 10% per year. How much will be in the account after 1 year if interest is compounded:
(a) Yearly
(b) Semi-annually
(c) Quarterly
(d) Monthly
(e) Weekly
(f) Daily
(g) Hourly
(h) Every minute
Solution:
(a) yearly
A = C[1 + hih(t)]
= 1000[1 + (1)(0.1)]
= $1100 Answer
(b) Semi-annually
A = C[1 + hih(t)]2
= 1000[1 + (1/2)(0.1)]2
= $1102.5 Answer
(c) Quarterly
A = C[1 + hih(t)]4
= 1000[1 + (1/4)(0.1)]4
= $1103.81 Answer
(d) Monthly
A = C[1 + hih(t)]12
= 1000[1 + (1/12)(0.1)]12
= $1104.7 Answer
(e) Weekly
A = C[1 + hih(t)]52
= 1000[1 + (1/52)(0.1)]52
= $1105.06 Answer
(f) Daily
A = C[1 + hih(t)]365
= 1000[1 + (1/365)(0.1)]365
= $1105.155 Answer
(g) Hourly
A = C[1 + hih(t)]8760
= 1000[1 + (1/8760)(0.1)]8760
= $1105.17 Answer
(h) Every minute
A = C[1 + hih(t)]525600
= 1000[1 + (1/525600)(0.1)]525600
= $1105.1709 Answer
In the above example, note that as h goes smaller and smaller (daily, hourly every minute etc.) the value of accumulated amount takes a limiting value.