a)Mrs Lee wants to set up a saving plan for her daughter’s university education. She makes...

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a)Mrs Lee wants to set up a saving plan for her daughter’suniversity education. She makes deposits of $500 at the beginningof every 6 months, starting on her daughter’s 2nd birthday andcontinuing for 10 years. 4(a). Answer the following questionsregarding this annuity, using an annual interest rate of 7.8%compounded twice a year.
(i) What type of annuity is this?
(ii) What is the total number of deposits into the account?
(iii) What is the interest rate per period?
(iv) Write down an explicit expression for the future value ofthis annuity.
(v) Find the future value of this annuity and give the amount tothe nearest dollar.
b)Mrs Lee is aiming to have an amount of $24,000 in a newinvestment account 6 years from now. The bank offers an annual rateof interest of 7.5% compounded monthly. Find the amount of moneythat Mrs Lee has to invest now to yield $24,000 in 6 years’time.
c)On her daughter’s 13th birthday, Mrs Lee starts another savingplan: she wants to make a regular deposit at the end of each monthto an account which will yield $6000 at the end of 5 years. Thebank’s interest rate is 7.5% p.a. compounded monthly. Find theamount of the regular monthly deposit needed, to the nearestdollar.

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Answer a i She makes deposits at the beginning of every 6 months Hence it is Annuity due or annuity in advance ii She makes deposits at the beginning of every 6 months for 10 years Hence number of See Answer

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a)Mrs Lee wants to set up a saving plan for her daughter’suniversity education. She makes deposits of $500 at the beginningof every 6 months, starting on her daughter’s 2nd birthday andcontinuing for 10 years. 4(a). Answer the following questionsregarding this annuity, using an annual interest rate of 7.8%compounded twice a year.(i) What type of annuity is this?(ii) What is the total number of deposits into the account?(iii) What is the interest rate per period?(iv) Write down an explicit expression for the future value ofthis annuity.(v) Find the future value of this annuity and give the amount tothe nearest dollar.b)Mrs Lee is aiming to have an amount of $24,000 in a newinvestment account 6 years from now. The bank offers an annual rateof interest of 7.5% compounded monthly. Find the amount of moneythat Mrs Lee has to invest now to yield $24,000 in 6 years’time.c)On her daughter’s 13th birthday, Mrs Lee starts another savingplan: she wants to make a regular deposit at the end of each monthto an account which will yield $6000 at the end of 5 years. Thebank’s interest rate is 7.5% p.a. compounded monthly. Find theamount of the regular monthly deposit needed, to the nearestdollar.