Question

A person invests Rs. 10,000 at 10 percent interest compounded annually. If An represents the amount at the end of n years, find a recurrence relation and initial condition that define the sequence {An}. Using the recurrence relation find amount payable after five years.

Answer 1

According to formula,
An = P( 1 +r/100)ⁿ
Where A is total amount after n years , r is the rate. P is the amount initially

An =10, 000( 1 + 10/100)ⁿ
=10,000( 1 +0.1)ⁿ
=10,000(1.1)ⁿ

An =10,000(1.1)ⁿ

now, put n = 1
A1 =10, 000(1.1),
put n =2 ,
A2 =10,000(1.1)²

in the same way ,
A3 =10, 00(1.1)³

you can see that
A2/A1 = A3/A2

so, {An} is in Geometric progression .

now,
amount payable after 5years

A5 =10,000(1.1)^5
=16, 105.1 Rs

Answer 2

According to formula,

According to formula,An = P( 1 +r/100)

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initially

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2so, {An} is in Geometric progression.

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2so, {An} is in Geometric progression.now,

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2so, {An} is in Geometric progression.now,amount payable after 5years

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2so, {An} is in Geometric progression.now,amount payable after 5yearsA5 =10,000(1.1)^5

According to formula,An = P( 1 +r/100)Where A is total amount after n years, r is the rate. P is the amount initiallyAn =10, 000( 1 + 10/100)=10,000( 1+0.1)"=10,000(1.1)An =10,000(1.1)now, put n = 1 A1 =10, 000(1.1), put n =2, A2 =10,000(1.1)2in the same way, A3 =10, 00(1.1)you can see that A2/A1 = A3/A2so, {An} is in Geometric progression.now,amount payable after 5yearsA5 =10,000(1.1)^5=16, 105.1 Rs