Question

Could someone help me solve this? I got it incorrect

Answer 1

`22.1\text{ years}`

Step-by-step explanation:

Here, we want to get the time taken to triple the deposit

The general formula to calculate future value is:

`A\text{ = P\lparen1 + }(r)/(n))\placeholder{⬚}^(nt)`

where:

P is the amount deposited

A is the future value, we have it as 3 * P here = 3P

r is the interest rate which is 5.1% = 5.1/100 = 0.051

n is the number of times interest is compounded per year which is 1

t is the number of years that we want to calculate

Substituting the values, we have:

`\begin{gathered} 3P\text{ = P\lparen1 + }(0.051)/(1))\placeholder{⬚}^(1* t) \\ \\ 3\text{ = 1.051}^t \\ ln\text{ 3 = t ln 1.051} \\ t\text{ = }\frac{ln\text{ 3}}{ln\text{ 1.051}}\text{ = 22.086} \end{gathered}`

To the nearest tenth of a year, we have this as 22.1 years