Help me with math please

Question

What amount P should be invested at 8% per annum, compounded annually, so that $2000 will be available after 7 years?

Answer 1

Find the Principal, that will give you 2000 at 8% interest,

compounded annually, for 7 years.

SOLUTION:

A = P(1+r)^t

2000 = P(1 + .08)^7

2000 = P(1.08)^7

P = 2000/(1.08^7)

P = 1166.98

If you invest $1166.98 at 8% interest, compounded annually,

for 7 years, you will end up with $2000.

Answer 2

Start with the equation for calculating compound interest: A = P(1+r/n)^nt

Since the account is compounded annually, n equals 1. If you plug in 1 for n in this equation, it becomes:

A = P(1+r)^t

Next, use algebra to solve the equation for P. To do so, divide both sides of the equation by (1+r)^t

P = A/(1+r)^t

Substitute in values for the variables. Remember to convert the interest rate to a decimal (r = 8/100 = 0.08).

P = 2000/(1+0.08)⁷

= 2000/(1.08)⁷ The order of operations states to evaluate the exponent before division

= 1166.98

The principal amount that should be invest is $1166.98