Question

In: Economics

Given a building its initial value is 2,000,000 SR at the first 5 years simple interest...

Given a building its initial value is 2,000,000 SR at the first 5 years simple interest rate is = 10 % and at the second 5 years compound interest rate is = 8 %.
1) Find the future value of this building after: A) 7 years old, and B)10 years old.
2) If the future value of this building after 10 years is 4,000,000 SR find its initial value now. 3) If the initial value is 2,000,000 SR and future value of this building is 5,000,000 SR find total years old of this building.

Solutions

Expert Solution

1 Future value of this building after : A) 7 years old

Initial value: 2000000 SR

First 5 years simple interest rate is= 10 %

Second 5 years compound interest rate is= 8 %

Simple interest for first 5 years

Simple interest(SI) = Principal x Rate of Interest x Time(years) / 100

SI= 2000000 x 10 x 5 / 100

SI= 10000 SR

Building value after 5 years= 2000000+10000= 2010000 SR

New principal= 2010000 SR

Time= 2 Years

Rate of interest= 8%

Compound Interest(CI)= Principal(1+R/100)T

CI= 2010000(1+8/100)2

CI= 2010000(1+0.08)2

CI= 2010000 x 1.08 x 1.08

CI= 2344464 SR

Future value of this building after : A) 7 years old= New principal+ Compound interest for next 2 years= 2010000+ 2344464= 4354464 SR

Find the future value of this building after: B)10 years old.

Compound interest for next 5 years= Principal(1+R/100)T

New principal after 5 tears= 2010000 SR

CI= 2010000(1+8/100)5

CI= 2010000(1+0.08)5

CI= 2010000 x 1.08 x 1.08 x 1.08 x 1.08 x 1.08

CI= 2953349.434

Future value of this building after: B)10 years old: New principal+ Compound interest for next 5 years= 2010000+2953349.434= 4963349.434 SR

2 If the future value of this building after 10 years is 4,000,000 SR find its initial value now.

Rate of interest= 10%

We assume its initial value: 2000000 SR

Simple Interest= Future value- Initial value

Simple interest(SI)= 4000000-2000000

SimpIe Interest(SI)= 2000000

It is based on Simple interest formula

Simple interest(SI) = Principal x Rate of Interest x Time(years) / 100

Principal(Initial value)= SI x 100/ R x T

Principal(Initial value)= 2000000 x 100/ 10 x 10

Principal(Initial value)= 2000000 SR

3) If the initial value is 2,000,000 SR and future value of this building is 5,000,000 SR find total years old of this building.

Simple Interest= Total value(Principal+ Simple interest)- Initial value

Simple Interest= 5000000-2000000= 3000000 SR

Principal/Initial value= 2000000 SR

Rate of interest= 10%

Simple interest(SI) = Principal x Rate of Interest x Time(years) / 100

Time= SI x 100/Principal x Rate of interest

Time= 3000000 x 100/2000000 x 10

Time= 15 Years.

Rahul Sunny answered 2 years ago
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