Months to Andrew's initial deposit will grow to $543 is 15 months
Compound interest is the interest paid on both principal and interest, compounded at regular intervals. At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal.
Formula of compound interest:
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
where,
A = final amount
P = principal amount
r = rate per annum
n = time in years
According to the question
Andrew deposited (P) = $500
interest rate of compounded continuously (r) = 6.5%,
for changing it into rate per month = 6.5% /12
Final Amount = $543
Now,
Applying Formula of compound interest:
[tex]A = P (1+\frac{r}{100} )^{n}[/tex]
substituting the value
[tex]543 = 500 (1+\frac{6.5}{12*100} )^{n}[/tex]
1.086 = [tex](1+\frac{6.5}{12*100} )^{n}[/tex]
1.086 = [tex]( 1.005416 )^{n}[/tex]
n ≈ 15 months (approx.)
Hence, Months to Andrew's initial deposit will grow to $543 is 15 months
To know more about compound interest here:
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