Question

100 POINTS You are planning to go on this trip in 2 years. How much money will you need to invest at a 1.55% interest rate compounded annually in order to have $2500 in 2 years? Use the compound interest formula A = P (1 + i)n. (Round final answer to the nearest cent, but otherwise don’t round any intermediate values)

Answer 1

`\huge \boxed{ \$ \ 2424.27}`

Explanation:

`\sf A=P(1+r)^n \\\\\\ A=final \ amount \\\\ P=principal \ amount \\\\ r=rate \ (\%) \\\\ n=number \ of \ years`

Applying the formula to solve for the principal amount.

`\sf 2500=P(1+1.55\%)^2`

`\sf 2500=P(1.0155)^2`

`\sf 2500=P(1.03124025)`

Dividing both sides by 1.03124025.

`\displaystyle \sf (2500)/(1.03124025) =(P(1.03124025))/(1.03124025)`

`\sf P=2424.26534457...`

The money to be invested would be $ 2424.27 (to nearest cent).

Answer 2

P = $ 2,424.27

Explanation:

Calculate rate of interest in decimal, solve for r

r = n[(A/P)^(1/nt) - 1]

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period