Answer :
The principal sum to be deposited is $ 551.26
Solution:
Given that,
Amount after 10 years = $ 1000
Rate of Interest = 6 % compounded quarterly
Number of years = 10 years
Principal = ?
The formula for compound interest, including principal sum, is:
[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Since interest is compounded quarterly, n = 4
[tex]r = 6 \% = \frac{6}{100} = 0.06[/tex]
Substituting the values in formula,
[tex]\begin{aligned}&1000=p\left(1+\frac{0.06}{4}\right)^{4 \times 10}\\\\&1000=p(1+0.015)^{40}\\\\&1000=p(1.015)^{40}\\\\&1000=p \times 1.8140\\\\&p=\frac{1000}{1.8140}=551.26\end{aligned}[/tex]
Thus the principal sum to be invested is $ 551.26
Answer:
551.26
Step-by-step explanation:
I just did it on my calculator so I’m not sure abt the steps
but I hope I helped.