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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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