Question

Suppose $1,500 is compounded weekly for 46 years. If no other deposits are made, what rate is needed for the balance to triple in that time?

Answer 1

The rate is needed is 1.037%.

Explanation:

Given : Suppose $1,500 is compounded weekly for 46 years. If no other deposits are made.

To find : What rate is needed for the balance to triple in that time?

Solution :

Applying compound interest formula,

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

Where, P is the principal

A is the amount

The balance to triple in that time i.e. A=3P

r is the rate

t is the time t=46 years

Compounded weekly so n=52

Substitute the value in the formula,

`3P=P(1+(r)/(52))^(52* 46)`

`3=(1+(r)/(52))^(2392)`

Taking log both side,

`\log 3=2392\ log(1+(r)/(52))`

`(\log 3)/(2392)=\ log(1+(r)/(52))`

`0.00019946=\ log(1+(r)/(52))`

Taking exponential both side,

`e^(0.00019946)=1+(r)/(52)`

`1.000199-1=(r)/(52)`

`0.000199=(r)/(52)`

`r=0.000199* 52`

`r=0.010372`

Into percentage,

`r=0.010372* 100`

`r=1.0372`

Therefore, the rate is needed is 1.037%.