The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.
Step-by-step explanation:
The given is,
Compounds money quarterly
Double your money in 10 years
Step:1
Formula to calculate future investment with compounded quarterly,
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]...............................(1)
Where, A - Future amount
P - Initial investment\
r - Rate of interest
n - No. of compounding in a year
t - No. of years
Step:2
Let, P = X
A = 2X ( Double your money )
From given, n - 4 ( for compounding quarterly )
t - 10 years
From equation (1)
[tex]2X =X(1+\frac{r}{4} )^{(4)(10)}[/tex]
[tex]\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}[/tex]
[tex]2 =(1+\frac{r}{4} )^{40}[/tex]
Take root [tex]40^{th}[/tex] root on both side,
[tex]\sqrt[40]{2} = (1+\frac{r}{4} )[/tex]
[tex]1.017479692 = (\frac{4+r}{4} )[/tex]
[tex](1.017479692)(4) = (r+4)[/tex]
[tex]4.06992=(r+4)[/tex]
[tex]r = 4.06992 -4[/tex]
[tex]r =( 0.06992)(100)[/tex]
r = 6.992 %
Result:
The interest rate is 6.992%, if a bank advertises that it compounds money quarterly and that it will take Double your money in 10 years.
