Calculate the amount if 18,000 is invested at 15% compounded annually for 3 year
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Answer:
Sum=Rs.18000
Sum=Rs.18000Time =2 years
Sum=Rs.18000Time =2 yearsRate of intereast=15%
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n⇒A=Rs.18000(1+10015)2
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n⇒A=Rs.18000(1+10015)2⇒18000×100115×100115
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n⇒A=Rs.18000(1+10015)2⇒18000×100115×100115⇒Rs.23805
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n⇒A=Rs.18000(1+10015)2⇒18000×100115×100115⇒Rs.23805∴ Compound Interest =A−P
Sum=Rs.18000Time =2 yearsRate of intereast=15%A=P(1+100r)n⇒A=Rs.18000(1+10015)2⇒18000×100115×100115⇒Rs.23805∴ Compound Interest =A−P=Rs.23805−Rs.18000=Rs.5805
Step-by-step explanation:
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Calculate the amount if Rs 18,000 is invested at 15%
p.a. compounded annually for 3 years.
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Hint: Here, we need to find the amount for the given principal. We will use the formula for amount when a principal is compounded for a period of time. Then, we will simplify the expression to find the required amount. Amount is the money obtained after adding the principal amount to the interest incurred during a particular period of time.
Formula used:
The amount A
of an investment after t
years is given by A=P(1+rn)nt
, where P
is the amount invested, n
is the number of compounding periods in a year and r
is the interest rate compounded annually.
Complete step-by-step answer:
As the sum is compounded annually, the number of compounding periods in a year is 1.
Substituting n=1
, t=3
, P=18,000
and R=15%
in the formula A=P(1+rn)nt
, we get
A=18000(1+15%1)1×3
Simplifying the expression, we get
⇒A=18000(1+15%)3
Rewriting the percentage as a fraction, we get
⇒A=18000(1+15100)3
Taking the L.C.M. in the parentheses, we get
⇒A=18000(100+15100)3
Adding the terms in the numerator, we get
⇒A=18000(115100)3
Both 115 and 100 are divisible by 5.
Simplifying the fraction in the parentheses, we get
⇒A=18000(2320)3
The expression (2320)3
can be written as the product of 2320
, 2320
, and 2320
.
Therefore, we can rewrite the equation as
⇒A=18000×2320×2320×2320
Simplifying the expression by cancelling the common factors, we get
⇒A=9×231×232×232
Multiplying the terms in the expression, we get
⇒A=1095034
Writing the amount in decimal form, we get
⇒A=27375.75
Therefore, we get the required amount as Rs.27375.75
in decimal form.