Question

3) A graduating high school student decides to take two years off and work to save money for college. The student plans to invest all money earned in a savings account earning 8% (APR) interest, compounded quarterly. The student hopes to have $ 48,000 by the time school starts in 24 months. How much money will the student have to save each month? a) $1,808 b) $1,852 c) $1,864 d) $1,961

Answer 1

Here, the rate of interest (r) is 8%, time (t) is 24months = 2years, the amount (A) is $48000 and the principal amount is unknown. The principal is compounded quaterly.

Here,

A = P(1+r/4)^4t

48000 = P( 1+ .08/4)^4 * 2

48000 = P( 1+ .02)^8

48000 = P(1.02)^8

48000 = P ( 1.17165938100226)

P = 48000/ 1.17165938100226

P = 40,967.5378171255.

Hence, the savings which needs to be done should be = 40967.5378171255/12 = 1706.98074238023.

This is the minimum amount of savings the student needs to do. In the options above, all the amounts are greater than this, hence the student can choose any of the options above to do his savings. The student can either choose from options (a), (b), (c) and (d) as the amounts in the options are greater than the minimum savings amount which we have calculated.

Hence, the student can choose from any of the option above to get an amount of at least $48000 at the end of two years.