Question

What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months? Calculate the result to the nearest cent.

Answer 1

Given Information:

Annual interest rate = r = 10%

Accumulated amount = A = $6380.00

Semi-annual compounding = n = 2

Number of years = t = 38/12 = 19/6

Required Information

Principle amount= P = ?

Answer:

Principle amount= P = $4,684.05

Step-by-step explanation:

The principal amounts in terms of compound interest is given by

`$ P = (A)/((1 + i)^N) $`

Where

i = r/n

i = 0.10/2

i = 0.05

N = n*t

N = 2*19/6

N = 19/3

So, the principal amount is

`P = (6380.00)/((1 + 0.05)^(19/3)) \\\\P= \$4,684.05 \\\\`

Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.