Annunity of a math

Question

A company needs $5,700,000 in 10 years in order to expand their factory. How much should the company invest each week if the investment earns a rate of 4.1% compounded weekly?

Answer 1

To calculate the amount that the company should invest each week, we can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n))/r],

where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the total number of periods.

In this case, the payment per period is what the company needs to invest each week, and the interest rate is 4.1% compounded weekly. The total number of periods is 10 years times 52 weeks per year, which is 520 weeks.

So, we can plug in the values and solve for PMT:

PV = $5,700,000

r = 0.041/52 = 0.0007885 (weekly rate)

n = 520

$5,700,000 = PMT x [(1 - (1 + 0.0007885)^(-520))/0.0007885]

Solving for PMT, we get:

PMT = $5,700,000 / [(1 - (1 + 0.0007885)^(-520))/0.0007885)] PMT = $5,700,000 / 412.3476

PMT ≈ $13,838.67

Therefore, the company needs to invest approximately $13,838.67 each week to have $5,700,000 in 10 years, assuming a 4.1% weekly compounded interest rate.