an inverstment of 35000 is made for 5 years at 6% interest rate.find its compound interest and compound amount if it is compounded quartely.
Compound interest
=P[(1+r)^n-1]
where
P=present value
r=rate of interest per period = 0.06/4 = 0.015
n=number of periods = 5*4 = 20
Compound interest
=35000(1.015^20-1)
=?
Compound Interest:
P x (1+r/100)^n
(where
P= Principal (present value)
r= Rate of interest
n= number of periods {20[4(quarterly)*5]}
)
Working:
35000 X (1+6/100)^20
=112249.7415
≈112249.74
ANS: $112249.74
14,ooo at 4% for 9 months rounded to the nearest cent
To calculate the compound interest and compound amount, we can use the following formulas:
Compound Interest (CI) = P(1 + R/n)^(n*t) - P
Compound Amount (A) = P(1 + R/n)^(n*t)
Where:
P = Principal amount (initial investment)
R = Annual interest rate (in decimal)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount (P) is $35,000, the annual interest rate (R) is 6% (which is 0.06 in decimal form), and it's compounded quarterly, so the number of compounding periods per year (n) is 4. The investment is made for 5 years (t = 5).
Let's calculate the compound interest first:
CI = 35,000 * (1 + 0.06/4)^(4*5) - 35,000
= 35,000 * (1.015)^(20) - 35,000
≈ 35,000 * 1.3482 - 35,000
≈ 47,179.66 - 35,000
≈ $12,179.66
Therefore, the compound interest for this investment is approximately $12,179.66.
Now, let's calculate the compound amount:
A = 35,000 * (1 + 0.06/4)^(4*5)
= 35,000 * (1.015)^(20)
≈ 35,000 * 1.3482
≈ $47,179.66
Therefore, the compound amount after 5 years, compounded quarterly, is approximately $47,179.66.