Question

Please I need aclarify answers with details in all the questions. Thank you

1. Newborn baby Gregory, born today, has doting grandparents who education. They calculate that he will need S25,000 per year for 4 years beginning at age 18. In addition, they'd like to give him a lump sum of S50,000 at age 22 so he can buy a car for his graduation. They want to make 18 equal annual payments into a 10% interest-paying account (starting today and ending on Gregory's 17th birthday) that will just cover these plans. How much will they need to invest each year? want t o start saving for his college 2. In 1790 Benjamin Franklin left $4,600 each to the cities of Philadelphia and Boston. He stipulated that the money be invested and that the principal not be touched for 100 years a. If the money had been invested at 4%, compounded yearly, how much would each city have had in 1890? b. How much if it had been invested at 5%, compounded yearly? c. 3. Calculate the present value of $1,000 to be received at an interest rate of 7 the end of 8 years. Assume percent. 4. What is the effective annual percentage rate (EAR) of 12 percent compounded monthly? 5. If you deposit S10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years? 6. Your parents are planning to retire in 18 years. They currently have S250,000 and they would like to have S1,000,000 when they retire. What annual interest rate would they have to carn on their $250,000 in order to reach their goal, Assume they save no more money?

Answer 1

Note as per guidelines i need to answer only 1st question but still i am answering first 4 questions

1. Let the future value required at the beginning of age 18 be X

Therefore X = 25000 + (25000/1.1)+ (25000/1.21) + (25000/1.331) + (50000/1.4641)

X = 25000+22727.27273+20661.15702+18782.87+34150.67

Therefore X = $121321.9725

Therefore amount required at the beginning of age 18 = $121321.9725

Now , FV of annuity = P[(1+r)^n - 1/r]

121321.9725 = P[(1+0.1)^18 - 1 / 0.1]

121321.9725 = P[4.559917313/0.1]

Therefore P = 121321.9725/45.599173 = $ 2660.6178

Therefore amount to be invested each year = $2660.6178 i.e. $2660.62

2. FV = PV(1+r)^n

a) FV = 4600(1+0.04)^100 = 4600*50.50494818 = $ 232322.7616 i.e. $232322.76

b) FV = 4600(1+0.05)^100 = 4600*131.501258 = $ 604905.78609 i.e. $604905.79

3. FV = PV(1+r)^n

1000 = PV (1+0.07)^8

1000 = PV(1.718186)

PV = 1000/1.718186 = $582.0091046 i.e. $582.01

4. Let $100 be the PV invested, Compounded monthly means no of compounding = 12

FV = 100(1+(0.12/12))^1*12 = 100*1.12682503 = $112.682503

Therefore interest earned = $112.682503 - $100 = $12.682503

THerefore Effective annual percentage rate = 12.682503/100 = 0.126825 i.e. 12.6825%