Question

Tuition of $1036 will be due when the spring term begins in 11 months. What amount should a student deposit today, at 3.93%, to have enough to pay the tuition? The student should deposit $ (Simplify your answer. Round to the nearest dollar as needed)

Answer 1

SOLUTION :

Let the amount be deposited today be $ x .

If 3.93% is simple interest rate :

FV after 11 month should be = 1036 ($)

=> x (1 + 3.93/100 * 11/12) = 1036 ($)

=> x * 1.036025 = 1036 ($)

=> x = 1036 / 1.036025  ($)

=> x = 999.98 = 1000 ($) . 

If 3.93% rate is compounded monthly :

Monthly rate, r = 3.93/12 % = 0.3275 % = 0.003275 in decimals

=> (1+r) = 1.003275

n = 11 months

FV = x(1 + r)^n = x * 1.003275^11 

=> 1036 = x * 1.03662

=> x = 1036/1.003662 

=> x = 999.40 = 1000 ($) 

So, amount to be deposited today to have $1036 after 11 months = $ 1000 (ANSWER).