At what quoted annual interest rate must $134,000 be invested so that it will grow to be $459,000 in 15 years if interest is compounded weekly

8.21% per annum

Explanation:

Interest rate rate is price paid by a borrow for the use of money and the return earned by a lender for postponing his consumption in favour of investment.

Interest is computed in two ways; Simple interest and compound interest

Simple interest: This is the interest paid on the principal invested or borrowed. To calculate simple interest, we use the formula below:

SI = Principal * interest Rate (%) * Time.

If I invest $100 for 2 years at 5%. The SI = 100 * 5% * 2 = $10

Total interest = $10

Compound interest : This is the interest earned on both the principal amount plus any already earned interest i. e the compound amount.

For example, if an investment promises 5% per annum and I invested $100 for 2 years. My interest is computed as follows:

Interest earned per year will be as follows:

Year 1 = 5% * $100 = $5

Year 2 = (5% * 100) + (5% * $5) = $5.25

Total interest = $10.25.

You will observe that the interest under the compound interest is higher, because the interest in the second year is computed using the principal plus the already earned interest in year 1 i. e the compound amount.

The total worth of the investment after the the investment period is called the Future Value.

The amount invested today or borrowed is called the Present value.

The future value can be computed using this formula

FV=PV * 〖 (1+r/m) 〗^ (n*m).

In this question, we were given the Future Value (FV) and the present value (PV) but need to find the the rate. So we need to work back.

134000 * (1 + r/52) ^ (15*52) = 459000

(780√3.42573) - 1) * 52 (it is the 780th root of 3.42578)

r=0.00157*52

r=0.08214*100 (to convert to a percentage)

r=8.21%