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4 votes
7100 dollars is placed in an account with an annual interest rate of 5%. To the nearest tenth of a year, how long will it take for the account value to reach 26400 dollars ?

2 Answers

5 votes

Answer: x=26.9

Explanation:

User Sultan
by
8.0k points
2 votes

Answer:

After
26.91\ years the principle amount value will reach to
26400\ dollars.

Explanation:

Given that,

Principle Amount
(P)= 7100\ dollars

Rate of Interest
(R)=
5%

Total Amount
(A)= 26400\ dollars

If Principle Amount
(P)
=P\ dollars, Time
=t\ years, Rate of Interest
=R%
pa

when interest is compounded annually:

Total Amount after
t\ years
= P(1+(R)/(100)) ^(t)

Now,


A= P(1+(R)/(100)) ^(t)


26400=7100(1+(5)/(100)) ^(t)


3.7183=(1+0.05)^(t)


3.7183=(1.05)^(t)

taking log both sides, we get


ln(3.7183)=ln {(1.05)^(t)}


1.31327=t* ln(1.05)


1.31327=t* 0.04879


t=26.91

Therefore,

After
26.91\ years the principle amount value will reach to
26400\ dollars.

User Matthew Chung
by
7.9k points
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