Question

Alice invests some money into an account that pays 4.25% compound interest per annum.

Work out after how many years Alice will have doubled the investment.

Answer 1

To double her investment, it will take Alice about 16.28 years.

Step-by-step explanation:

To determine how long it will take for Alice to double her investment, we can use the formula for compound interest. The formula is given by:

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

Where:

• A is the final amount (twice the original investment)
• P is the principal amount (initial investment)
• r is the annual interest rate (4.25% or 0.0425)
• n is the number of times that interest is compounded per year (we assume it is compounded once per year)
• t is the number of years

Setting A equal to 2 times P, we can solve for t:

2P = P(1 + 0.0425/1)^(1t)

Dividing both sides by P:

2 = (1.0425)^t

Take the natural logarithm of both sides:

ln(2) = t ln(1.0425)

Now we can solve for t:

t = ln(2) / ln(1.0425)

Using a calculator, we find that t is approximately 16.28 years. Therefore, it will take Alice about 16.28 years to double her investment.