This is a finance math problem, TVM solver will be great to use!

Question

Lia saved $800 from his summer job and bought a GIC earning 3.25%, compounded monthly. She started an after school job in September and wants to have $3000 by next summer so she can go travelling. How much does she need to save from her pay every month for 9 months if she can deposit the money in an account earning 2.5%, compounded monthly?

Answer 1

Hi Lee.

It isn't clear when Lia bought the GIC so we can only assume it was at the same time she started her job.

Then, the total she will have after 9 months is the accumulated value of the GIC plus the value of each month's salary she deposits.

Value of the GIC after 9 months = 800 (1 + 3.25%/12)⁹

= 800(1 + 0.27%)⁹

= 800 x 1.0027⁹

= 800 x 1.02456

= $819.65 . . . . . . . . . (a)

Suppose she saves P dollars of her salary, each month for 9 months. This is an annuity of P for 9 months at a monthly interest rate, i, of 2.5%/12 = 0.208%.

The value of all deposits after 9 months = P ( (1+i)⁹ - 1) / i

= P (1.00208⁹ - 1) / 0.00208

= P (9.08) . . . . . . .(b)

Now, she needs the sum of (a) and (b) to be at least $3,000

=> 9.08P +819.65 >= 3000

=> 9.08P >= 2281.35

=> P >= 2281.35/9.08 = 251.25

She needs to save $251,25 each month for 9 months.