1. Compound
Interest
The Interest Rate and
Time

2. The interest rate can be determined
given the final amount (F), present value
(P), conversion period (m) and the total
number of periods (n) by using the following
formula:
Interest rate
𝑟 =
𝑛 𝐹
𝑃
− 1 (𝑚)(100%)
where r is derived from the formula
𝐹 = 𝑃(1 + 𝑖) 𝑛 and 𝑖 =
𝑟
𝑚
.

3. Example 1:
Find the rate compounded semi-
annually if P 9,000 accumulates to P 15,
500 in 4 years and 5 months.

4. Example 2:
At what rate compounded quarterly
will P 15, 000 accumulate to P 20,000 in 4
years and 6 months?

5. Time (t) can be computed, using
logarithms, if rate (r), amount (F) and
present value (P) of the investment are
given. The following formula will be used:
time
𝑡 =
log
𝐹
𝑃
𝑚[log(1 + 𝑖)]
where t is derived from the formula
𝐹 = 𝑃(1 + 𝑖) 𝑛 and 𝑛 = 𝑡𝑚.

6. Example 1:
How long will it take P 16,000 to
amount to P 19,200 if the interest rate is
10% compounded semi-annually?

7. Example 2:
When will P 5, 500 accumulate to P
10,500 if invested at 15% compounded
quarterly?