Answer:
T is 13.9 years to the nearest 10th of a year
Explanation:
In this question, we are to calculate the number of years at which someone who invests a particular amount will have a particular amount based on compound interest.
To calculate the number of years, what we do is to use the compound interest formula.
Mathematically,
A = P(1+ r/n) ^nt
Where A is the final amount after compounding all interests which is $19,200 according to the question
P is the initial amount invested which is $10,000 according to the question
r is the rate which is 4.75% according to the question = 4.75/100 = 0.0475
n is the number of times per year in which interest is compounded. This is 2 as interest is compounded semi-annually
t= ?
we plug these values;
19200 = 10,000(1+0.0475/2)^2t
divide through by 10,000
1.92 = (1+0.02375)^2t
1.92 = (1.02375)^2t
We find the log of both sides
log 1.92 = log [(1.02375)^2t)
log 1.92 = 2tlog 1.02375
2t = log 1.92/log 1.02375
2t = 27.79
t = 27.79/2
t = 13.89 years
The question asks to give answer to the nearest tenth of a year and thus t = 13.9 years