You make monthly deposits of $5000 into an account that earns an annual rate of

Question

You make monthly deposits of $5000 into an account that earns an annual rate of 6%. What is the minimum number of months (n) it takes for the balance to reach $150,000. SHOW WORK!!! 150000 = 5000 (1 + 0.06/12)^n John wants to invest $100 per month into an account for 25 years. What is the minimum annual rate of return (compounded monthly) that will yield $100,000 for John. Give formula and solve by graphing or trial/error. No work needed. Answer: r to nearest hundredth of a percent: _____ You finance a brand new Maserati by agreeing to make monthly payments over a 5-yr period. The purchase price is $150,000 and the annual rate is 2.4% compounded monthly. The monthly payment is given below for your convenience. Complete the amortization table for the first two periods (no work needed): P M T = $2655.50 For the car above, how much total interest will you pay over the 5 years. Round to the nearest dollar amount.

Explanation / Answer

1) $5000 added in account monthly to reach $150.000 in n months

for first $5000 rupees : Final amount =5000*0.06/12 *n +5000

for second $5000 : final amount = 5000*0.06/12*n-1 +5000

similarly for n th month : final amount at end of one month =5000*0.06/12*1 + 5000

Total amount = 5000*0.06/12 *n +5000 + 5000*0.06/12*n-1 +5000 ........................+5000*0.06/12*1 +5000

= 5000*n + 5000*0.06/12 *[n +n-1 +n-2 ...1]

150000=5000n (1 +(0.06/12)*(n+1/2))

30 =n (1 + (n+1)(0.0025))

30 = n (1.0025 +0.0025n)

12000 =n (401 +n)

n2 +401n -12000 =0

n = 28 months

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