Respuesta :
Answer:
Apr=6.2%
Step-by-step explanation:
∵ Amount formula in compound interest,
[tex]A=P(1+r)^t[/tex]
Where,
P = initial value,
r = rate per period,
t = number of periods,
Here, the given expression that represents the amount of loan after 7 years,
[tex]A=4800(1.06)^7[/tex]
[tex]=4800(1+0.06)^7[/tex]
By comparing,
P = $ 4800, r = 0.06, t = 7 years,
If annual rate is 0.06, then, the rate per month = 0.06/12 = 0.005
Time = 7 × 12 = 84 months,
Hence, the amount would be,
[tex]A=4800(1+0.005)^{84}[/tex]
Let it is equivalent to the amount obtained in annual compound rate r for 7 years,
[tex]\implies 4800(1+r)^7=4800(1+0.005)^{84}[/tex]
[tex](1+r)^7=(1.005)^{84}[/tex]
Taking log both sides,
[tex]7\log (1+r) = 84 \log(1.005)[/tex]
[tex]\log(1+r)=\log(1.005)[/tex]
By graphing calculator,
r = 0.06168 ≈ 0.062 = 6.2 %
