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Declan invested an amount of money in a savings account that pays compound interest at a rate of 8% per annum. After 14 years, there is £14,685.97 in the savings account (rounded to the nearest 1.d.p). How much money did Declan originally invest? Give your answer to the nearest £1

Sagot :

To determine the original amount of money Declan invested, we need to solve for the principal

P in the compound interest formula. The formula for compound interest is:

=

(

1

+

)

A=P(1+

n

r

​

)

nt

where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (decimal).

n is the number of times interest is compounded per year.

t is the number of years the money is invested or borrowed for.

Given:

=

14685.97

A=14685.97 pounds

=

8

%

=

0.08

r=8%=0.08 (per annum)

=

14

t=14 years

Since it is compounded annually,

=

1

n=1.

The formula simplifies to:

=

(

1

+

)

A=P(1+r)

t

Substitute the given values:

14685.97

=

(

1

+

0.08

)

14

14685.97=P(1+0.08)

14

14685.97

=

(

1.08

)

14

14685.97=P(1.08)

14

First, calculate

(

1.08

)

14

(1.08)

14

:

(

1.08

)

14

≈

2.937

(1.08)

14

≈2.937

Now substitute back into the equation:

14685.97

=

×

2.937

14685.97=P×2.937

Solving for

P:

=

14685.97

2.937

P=

2.937

14685.97

​

≈

5000

P≈5000

Therefore, the original amount of money Declan invested was approximately £5000.

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