Question

James has heard that it is important to start saving for retirement at an early age. He deposits $1000 on each of his birthdays from age 16 through to age 25 inclusive into an account that pays 10% interest compounded annually. How much will be in his account immediately following his 25th birthday? If James leaves this amount in the account for 35 more years, without making any further deposits, how much will be in the account when he turns 60 years old? Amount in account at age 25 (to the nearest dollar) 2. Amount in account at age 60 (to the nearest dollar) John, James' twin brother, doesn't want to start saving as early as his brother James. He decides, instead, to deposit $1000 on each of his birthdays from age 26 to age 60 inclusive. If he deposits his money into an account that pays 10% interest compounded annually, what will be in his account just after his 60th birthday? Did James or John have more money in their account at age 60? How much more did he have? How much money did James actually deposit? How much money did John actually deposit? Express your answers to the nearest dollar. Do not include the dollar sign in your answer. e.g. 4512.00 1. Twin with more money in his account at age 60 2. How much more he had than his brother 3. How much James deposited 4. How much John deposited Find the future value of the following annuity. Express your answer to two decimal places. Do not include the dollar sign in your answer Payments of $1000 are made each month for 3 years. Interest is 12% compounded monthly. Find the future value of the following annuity. Express your answer to two decimal places. Do not include the dollar sign in your answer. Payments of $600 are made each quarter for 8 years. Interest is 8% compounded quarterly

Answer 1

Sol: James Bank balance following 25th Birthday: using Future Value Annuity Formula: P* ((1+r)^n) - 1)/r, here r =0.10 n = 10 and P =1000 thus FV will be =15,937.42

James Bank Balance after 60 years if he earns rate @10% compounded annually for 35 years (60-25) the Value after 25 year of his deposit is $15,937. We will use Future Value Interest Formula = PV* (1+r)^n here PV=15937; r = 0.10 and n = 35 by using this formula the result will be = $ 447869

John James twin brother decides to deposit $1000 from Age 26 to Age 60 (inclusive) thus the term here will be 35 years, rate of interest 10% compounded annually to know what John bank balance will be after age 60 we will use Future Value Annuity Formula: P* ((1+r)^n) - 1)/r, here r =0.10 n = 35 and P =1000 thus FV will be = 271024.37 or $ 2,71,024

James have more money in his bank after 60 years i.e. 447869 > John Balance of 271024 thus James have 176845 more than John. James actual deposit was 1000*10= 10000.00. John actual deposit: 1000*35 = 35000.00

Sol: For a deposit of $1000 per month for a period of 3 years and yielding 12% compounded monthly. We have to find the Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 12%/12= 1% or 0.01 n = 3 *12 = 36 and P =1000 thus FV will be = 43076.88

For a deposit of $600 per quarter for a period of 8 years and yielding 8% compounded quarterly. We have to find the Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 8%/4= 2% or 0.02 n = 8*4 = 32 and P =600 thus FV will be = 26536.22

For a deposit of $10000 semi annually for a period of 9 years and yielding 9% compounded semi-annually. We have to find the Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 9%/2= 4.50% or 0.045 n = 9*2 = 18 and P =1000 thus FV will be = 268550.84

For a desired sum of 2500 which is our Future Value Annuity, periodic payment at the end of each quarter for 4 years will make N= 16; the rate is 6% compounded quarterly so r= 1.50% or 0.015, we have to use Future Value annuity formula: FV =P* ((1+r)^n) - 1)/r; 2500= P* ((1+0.015)^16) -1)/ 0.015 this will result in periodic payment of 139.41

For a desired sum of 54000 which is our Future Value Annuity, periodic payment at the end of year for 25 years will make N= 25; the rate is 6% compounded year so r= 6.00% or 0.06, we have to use Future Value annuity formula: FV =P* ((1+r)^n) - 1)/r; 54000= P* ((1+0.06)^25) -1)/ 0.06 this will result in periodic payment of 984.24

Billy deposits periodically $1000 at each year end for 10 years @ 8% annual compounding thus we have to use Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 9% or 0.09 n = 10 and P =1000 thus FV or Amount in Account after final deposit will be = 15192.93 and Interest Earned is = Amount in the Account after final deposit 15192.93 - Total Deposit i.e. 1000*10=10000 thus interest = 5192.93

Twyla Twotimer deposit of $500 semi annually for a period of 10 years and yielding 8% compounded semi-annually. We have to find the Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 8%/2= 4.00% or 0.04 n = 10*2 = 20 and P =500 thus FV or Amount in Account after final deposit will be = 14889.04

Jessica deposit of $500 quarterly for a period of 7 years and yielding 9% compounded quarterly. We have to find the Future Value annuity of this deposit formula: P* ((1+r)^n) - 1)/r, here r = 9%/4= 2.25% or 0.0225 n = 7*4 = 28 and P =500 thus FV or Amount in Account after final deposit will be = 19212.11