a) Jamie, who is 13 years old, wants to make deposits into an account to accumul
ID: 2659653 • Letter: A
Question
a) Jamie, who is 13 years old, wants to make deposits into an account to accumulate money for a new car when she is 18 years old. At that time, she will need $25,000. If her account pays interest at 6.2% per year compounded quarterly and deposits are made at the end of each quarter, how large much each deposit be in order to reach her goal? (Round to the nearest cent.)
b) Chris plans to sell his current home and use the proceeds to cover the cost of a new home. He decides to take out a short-term loan to help with expenses until his current house sells. If the bank charges 9% simple annual interest, how much will Chris owe at the maturity of a 120-day loan of $100,000? Assume the bank counts a year as 360 days. (Round to the nearest dollar).
c) An investment of $8215 was made into an account that compounded interest monthly. At the end of 14 years, the balance in the account doubled. Find the interest rate to the nearest tenth of a percent.
Explanation / Answer
a) Jamie, who is 13 years old, wants to make deposits into an account to accumulate money for a new car when she is 18 years old. At that time, she will need $25,000. If her account pays interest at 6.2% per year compounded quarterly and deposits are made at the end of each quarter, how large much each deposit be in order to reach her goal? (Round to the nearest cent.)
fv =25000, pv =0 , nper = 5*4 = 20 , rate =6.2/4 = 1.55%
Deposit Amount= pmt(rate,nper,pv,fv)
Deposit Amount= pmt(1.55%,20,0,25000)
Deposit Amount= $ 1075.83
b) Chris plans to sell his current home and use the proceeds to cover the cost of a new home. He decides to take out a short-term loan to help with expenses until his current house sells. If the bank charges 9% simple annual interest, how much will Chris owe at the maturity of a 120-day loan of $100,000? Assume the bank counts a year as 360 days. (Round to the nearest dollar).
Chris will owe at the maturity = 100000*9%*120/360 + 100000 = $ 103000
c) An investment of $8215 was made into an account that compounded interest monthly. At the end of 14 years, the balance in the account doubled. Find the interest rate to the nearest tenth of a percent.
pv =8215 , fv =16430, nper = 14*12 = 168 , pmt =0
Monthly Interest rate = rate(nper,pmt,pv,fv)
Monthly Interest rate = rate(168,0,-8215,16430)
Monthly Interest rate = 0.4134%
Annual Interest Rate = 4.96% compounded interest monthly
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