**Q5: **

The loan amount and the monthly payment on the loan are related by the formula
where is the loan amount, is the monthly payment,
is the monthly interest rate, and is the
number of months over which the loan will be repaid.

A kitchen dealer is offering 6-year loans with a monthly interest rate of
.

Use the formula to calculate, to the nearest cent, the monthly payment on a
kitchen costing , with no down payment.

A customer who wishes to buy the kitchen can afford payments of $250 per month.
Calculate the down payment they must make for the monthly payments to be affordable.
Give your answer to a suitable degree of accuracy.

**Q10: **

To calculate the amount of money in a structured savings account, where a saver deposits
a regular amount at regular time intervals, we consider each monthβs deposit separately.

Consider a saver who makes a regular deposit on the last day of every month in an account
where the interest is calculated on the last day of every month.

Let the regular deposit be , and let the monthly interest rate be (an interest rate of would give an value of ).

On the day the th deposit is made, the first deposit has been earning interest for
months, so its value is .

Similarly, on the day the th deposit is made, the second deposit has been earning
interest for months, so its value is .

The pattern continues until we consider the th deposit which has earned no interest on
the day it is deposited so its value is .

To calculate the total amount in the fund, , on the day the th deposit is made, we need
to find the sum of the values of the individual deposits.

Starting with the th deposit, we get

What kind of series do you see on the right-hand side of the equation?

- Ageometric
- Barithmetic
- Charmonic
- DFibonacci

Using the formula for the sum of the first terms of a geometric series, write a
formula for , the total amount in the fund.

- A
- B
- C
- D
- E

**Q12: **

A couple want to buy an apartment for . The monthly mortgage payment can be calculated using the formula

where is the monthly payment, is the loan amount, is the monthly interest rate, and is the number of months over which the mortgage will be repaid.

The bank offers a 20-year mortgage with an interest rate of per month, and they have a down payment of . Calculate the monthly payment to the nearest cent.

What should the down payment be, to the nearest 100 dollars, if the couple can afford to pay only per month?

Instead of increasing the down payment, they decide to increase the mortgage term. Assuming the same rate of interest, can they afford to make the monthly payments on a 25-year mortgage?