Mathematics, 01.04.2020 04:12, alandrabell9234

A bank advertises that it compounds money quarterly and that it will take Double your money in 10 years. what is the interest-rate?

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Answers

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,

$A =P(1+\frac{r}{n} )^{nt}$ ...............................(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)

$2X =X(1+\frac{r}{4} )^{(4)(10)}$

$\frac{2X}{X} =(1+\frac{r}{4} )^{(4)(10)}$

$2 =(1+\frac{r}{4} )^{40}$

Take root $40^{th}$ root on both side,

$\sqrt[40]{2} = (1+\frac{r}{4} )$

$1.017479692 = (\frac{4+r}{4} )$

(1.017479692)(4) = (r+4)

4.06992=(r+4)

r = 4.06992 -4

r =( 0.06992)(100)

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.

answered: Guest

Where is the problems

answered: Guest

Idon’t know what the answer is i wish i could

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A bank advertises that it compounds money quarterly and that it will take Double your money in 10 ye...