Question

A bank account pays 4.6​% annual​ interest, compounded monthly. How much must be deposited now so that the account contains exactly ​$18 000 at the end of one year​?

Answer 1

Let the amount that should be deposited now be 'X'. A= X(1+r/n)^nt where, A is amount accumulated at the end of one year. r is the interest rate per month, t is no.of years and n is nunber of times interest is compounded in a year.

So A=$18000, r= 0.3833..% (4.6%/12), t= 1year and n=12.

$18000=X(1+0.38333/12)^12×1 ​​​ $18000=X(1.38333)¹² ​​​​​​. $18000=X(1.04698233309) X=$18000/1.04698233309. X= $17192.27

Therefore, $17792.27 has to be deposited now to get exactly $18000 in the account after one year.