# A bank deposit paying simple interest at the rate of 5%/year grew to a sum of $3100 in 10 months. Find the principal

1) A bank deposit paying simple interest at the rate of 5%/year grew to a sum of $3100 in 10 months. Find the principal.

2) RETIREMENT FUNDS: Five and a half years ago, Chris invested $10,000 in a retirement fund that grew at the rate of 10.82%/year compounded quarterly. What is his account worth today?

3) SAVINGS ACCOUNTS: If Jackson deposits $100 at the end of each month in a savings account earning interest at the rate of 8%/year compounded monthly, how much will he have on deposit in his savings account at the end of 6 years, assuming that he makes no withdrawals during that period.

4) PURCHASING A HOME: The Johnsons have accumulated a nest egg of $40,000 that they intend to use as a down payment toward the purchase of a new home. Because their present gross income has placed them in a relatively high tax bracket, they have decided to invest a minimum of $24000/month in a monthly payment (to take advantage of the tax deduction) toward the purchase of their house. However, because of other financial obligations, their monthly payments should not exceed $3,000. If local mortgage rates are 8%/compounded monthly for a conventional 30-year mortgage, what is the price range of houses that they should consider?

5) Find the periodic payment R required to amortize a loan of P dollars over t yr with interest charged at the rate %/year compounded m times a year....P=80,000, r=10.5, t=15, m=12

6) LOAN AMORTIZATION: What monthly payment is required to amortize a loan of $30,000 over 10 yr if interest at the rate of 12%/year is charged on the unpaid balance and interest calculations are made at the end of each month?

7) SINKING FUNDS: The management of Gibraltar Brokerage Services anticipates capital expenditure of $20,000 in 3 yr for the purchase of new computers and has decided to set up a sinking fund to finance this purchase. If the fund earns interest at the rate of 10%/year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund.

8) FINANCING A HOME: Sarah secured a bank loan of $200,000 for the purchase of a house. The mortgage is to be amortized through monthly payments for a term of 15 yr, with an interest rate of 6%/year compounded monthly on the unpaid balance. She plans to sell her house in 5 years. How much will Sarah still owe on her house?

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#### Solution Preview

1) A bank deposit paying simple interest at the rate of 5%/year grew to a sum of $3100 in 10 mo. Find the principal

Assume the principal is x dollars.

Then x+x*0.05*(10/12)=3100.

X=2976 dollars.

Therefore, the principal is 2976 dollars.

2) RETIREMENT FUNDS: Five and a half years ago, Chris invested $10,000 in a retirement fund that grew at the rate of 10.82%/year compounded quarterly. What is his account worth today?

F=10000*(1+0.1082/4)^(5.5*4)= 17989.33 dollars.

Therefore, his account is worth 17989.33 dollars today.

3) SAVINGS ACCOUNTS: If Jackson deposits $100 at the end of each month in a savings account earning interest at the rate of 8%/year compounded monthly, how much will he have on deposit in his savings account at the end of 6 years, assuming that he makes no withdrawals during that period.

For the first month, F1=100

For the second month, F2=100*(1+0.08/12)+100

For the third month, F3=100*(1+0.08/12)^2+100*(1+0.08/12)+100

For the nth month, Fn=100+100*(1+0.08/12)+100*(1+0.08/12)^2+...+100*(1+0.08/12)^(n-1)

=100*[(1+0.08/12)^n-1]/(0.08/12)

When n=6*12=72, ...

#### Solution Summary

A bank deposit paying simple interest at the rates are examined.