Question

T-Mobile Wi-Fi 11:57 AM Close Homework for April 9.pdf Homework for Class #3-April 9-(20 points) Do the problems 0ค separate paper, use penciL Show all compatations. Begin wath the Homework is due at beginning of dass Not acepted after class begins m da whereindcสed. ST-2 FUTURE VALUE it is now January 1, 2014 Today you wil deposit $1,000 into a wings account that pays 8%. a If the bank compounds interest annually, how much will you have in your account on January 1, 20177 b. What will your January 1, 2017, balance be if the bank uses quarterly compounding? C. Suppose you deposit $1,000 in three payments of $333 333 each on January 1 of2015, 2016, and 2017. How much will you have in your account on January 1,2047, based on 8% annual compounding? d. How much will be in your account if the three payments begin on January 1, 20347 Suppose you deposit three equal paryments into your account on January 1 of 2015, 2016, and 2017. Assuming an 8% interest rate, how large must your payments be to have the same endng balance as Part a? 5-1 FUTURE VALUE you deposit $10.000 in wil be in your account afber 5 years? bank account that pays 10% interest annually, how much 54TIME FOR A LUMP SUM TO DOUBLE If you deposit money today inan account that pays 6 S interest, how long will it take to double your money? annual -11 GROWTH RATES Shalit Corporation's 2013 sales were $12 milion. its 2008 sales were 56 million a. At what rate have sales been growing? b. Suppose someone made this statement "Sales doubled in 5 years. This represents a growth of 100% în 5years so, dividing 100% by S, wefind the growth rate to be 20% per year. Is the statement correct? S-13 TIME FOR A LUMP SUM TO DOUBLE How long will it take $200 to double if it eares the following rates? Compoundingoccurs once a year a, 7% b.20% c. 18% PERIODS Find the amount to which $500 wil grow under each of these conditions a, 12% compounded annually for 5 years b, 12% compounded semiannually for 5 years C. 12% compounded quarterly for 5 years d 12% compounded monthly for years e, 12% compounded daily for 5 years t why does thオobserved pattern of PVs occur?

Answer 1

Since there are multiple questions, I would limit myself to answering the first questuon.

It is a simple case of compound interest.

A = P (1+r)^n

Where

A is amount, P is principal,r is rate of interest and n is number of time periods

In first case, total amount is 1,000* (1+0.08)^3 = 1259.71

In second case, the bank does quarterly compounding, hence rate per quarter is = 8/4 = 2% compounded over 3*4= 12 quarters

Hence total amount = 1,000*(1+0.02)^12 = 1268.24

In third case, since the amounts are invested over 3 years, the first installment gets compounded thrice while the second and third installments are compounded twice and once respectively.

Hence total amount :

Year 1 amount (1000/3)*(1.08)^3 = 419.90

Year 2 amount (1000/3)*(1.08)^2 = 388.8

Year 3 amount (1000/3)*1.08 = 360

Hence total maturity amount = 1168.7