# Required amount to invest now in a trust fund (difficulty with discount rate)

The parents of three children aged 1, 3, and 6 wish to set up a trust fund that will pay 25k to each child upon attainment of age 18, and 100k to each child upon attainment of age of 21.

Assume that the trust fund will grow at nominal annual interest rate of 3.2% convertible monthly for the first four years, effective annual interest rate of 3.5% for the next year, nominal annual rate of discount of 4.5% compounded quarterly for the next seven years and effective annual rate of discount at 5.25% thereafter.

What amount must the parents now invest in the trust fund in order to pay 25k to the child aged 6 upon attainment of age 18, and 100k to the child aged 6 upon attainment of age 21?

- So i tried to calculate each type of interest alone, and assumed we're trying to find the present value:

• I first multiply 25k by the three first type of interest rate in the question, to which we reach age of 18, then add 100k multiplied by the 4 type of interest given in the question.

Type 1: nominal annual interest rate of 3.2% convertible monthly: 1/(1+0.032/12)^12months * 4 years

Type 2: effective annual interest rate of 3.5%: 1/(1+0.035)^1 year

From here i block, i don't know how to calculate the nominal annual rate of discount of 4.5% compounded quarterly for seven years and effective annual rate of discount of 5.25%.

I'm having difficulties understanding different between a present value and a discounted rate. As for nominal rate, from what i understood it's simple the annual interest rate but given under different time (monthly, or semi annually, etc).

I would really really appreciate some help on this as i tried hard to understand and it's a bit a confusing. Thank you

• The growth factor in case of the effective annual interest rate of 3.5% for the next year is just $1.035$ – callculus Feb 18 at 10:01
• No it's not, we're asked for the preset value, so it has to be ^-1 the effective annual interest rate. But thanks for not answering the actual question. – xim Feb 18 at 13:47
• What? Have you noticed that you haven´t marked the most answers as accepted. It doesn´t motivate people to answer your questions. – callculus Feb 18 at 14:21