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.

Question

asked Dec 18, 2024 166k views

1 Answer

Spraff · Answer 1 · 2024-12-22T04:46:55+0000

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

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.