Question

Mr tan invested 5000 Swiss francs(CHf) bank A at a nominal annual interest rate of r% compounded monthly, for four years. The total interest he received was 1866 CHF.

A) calculate value of r
Mr black invested 5000 CHF in a Bank at a nominal annual interest rate of 3.6% compounded quarterly for four years
B)calculate the total interest he received at the end of the four years give your answer two decimal places.

Answer 1

(A)

We are given

Mr tan invested 5000 Swiss francs(CHf) bank

so,

`P=5000`

nominal annual interest rate of r% compounded monthly

so, n=12

t=4

total interest he received was 1866 CHF

I=1866

we can use formula

`I=P(1+(r)/(n) )^(nt)-P`

now, we can plug values

`1866=5000(1+(r)/(12) )^(12*4)-5000`

now, we can solve for r

`r=0.0795`

so, interest rate is 7.95%..........Answer

(B)

we are given

P=5000

r=0.036

n=4

t=4

so, we can use interest formula

`I=P(1+(r)/(n) )^(nt)-P`

now, we can plug values

`I=5000(1+(0.036)/(4) )^(4*4)-5000`

now, we can simplify it

and we get

`I=770.702`

The total interest is 771 CHF...........Answer

Answer 2

Given : Invested amount = $5000.

Rate of interet = r% compunded monthly.

Number of years = 4 years.

Total interest received = $1866.

Therefore, total amount after 4 years = 5000+1866 = $6866.

We know, formula for compound interest :

`A=P(1+(r)/(n))^(t* n)`, where P is the invested amount, n is the number of monthly installments in an year.

Number of months in an year are 12.

Plugging n=12, P=5000, t=4 in the formula now, we get

`6866=5000{(1+(r)/(12))^(12* 4)`

`6866=5000{(1+(r)/(12))^(48)`

Dividing both sides by 5000, we get

`(6866)/(5000) =(5000)/(5000) {(1+(r)/(12))^(48)`

`(6866)/(5000) = {(1+(r)/(12))^(48)`

`1.3732= {(1+(r)/(12))^(48)`

Taking 48th root on both sides, we get

`\sqrt[48]{1.3732} = \sqrt[48]{(1+(r)/(12))^(48)}`

`\sqrt[48]{1.3732}=\left(1+(r)/(12)\right)`

`1.00662903758=1+(r)/(12)`

Subtracting 1 from both sides, we get

0.00662903758 =
`(r)/(12)`

Multiplying by 12 on both sides, we get

r=0.07954845101

r≈0.0795

Or 7.95%.

A) The value of r is 7.95% compounded monthly.

Now, we need to find the interest after four years if the rate of interest is 3.6% compounded quarterly.

There are 4 quarters in an year.

So, n=4 and r=3.6%= 0.036.

Plugging values in compound interest formula now, we get

`A=5000{(1+(0.036)/(4))^(4* 4)`

`\mathrm{Divide\:the\:numbers:}\:(0.036)/(4)=0.009`

`A=5000* \:1.009^(16)`

`A=5000* \:1.15414\dots`

`=5770.70222\dots`

A≈5770.70

Subtracting 5770.70 -5000.00 = 770.70.

B) Therefore, the total interest he received at the end of the four years upto two decimal places is $770.70.