Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years will be $25,000, approximately how much money is presently in the account?
Answer: $11,820
Step-by-step explanation:
The formula to calculate the compound amount after x years is given by :-
@@MATH_TOKEN_0@@, where r is the rate of interest.
Given: The accumulated value A= $25000
The rate of interest r= 4.25%=0.0425
Let P be the present value invested in the account.
Now,according to the question,we have
\(25000=P(1+0.0425)^{18}\\\\\Rightarrow\ 25000=P(2.11528624641)\\\\\Rightarrow\ P=\frac{25000}{2.11528624641}\\\\\Rightarrow\ P=11818.7314092\approx\$11820......[\text{to the nearest tens}]\)
Hence, the amount of money presently in the account =$11,820