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

Answer:

The rate is needed is 1.037%.

Step-by-step 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,

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

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,

$3P=P(1+\frac{r}{52})^{52\times 46}$

$3=(1+\frac{r}{52})^{2392}$

Taking log both side,

$\log 3=2392\ log(1+\frac{r}{52})$

$\frac{\log 3}{2392}=\ log(1+\frac{r}{52})$

$0.00019946=\ log(1+\frac{r}{52})$

Taking exponential both side,

$e^{0.00019946}=1+\frac{r}{52}$

$1.000199-1=\frac{r}{52}$

$0.000199=\frac{r}{52}$

$r=0.000199\times 52$

$r=0.010372$

Into percentage,

$r=0.010372\times 100$

$r=1.0372$

Therefore, the rate is needed is 1.037%.