New Zealand
Level 6 - NCEA Level 1

# Differing frequencies (payments and compounding interest)

## Interactive practice questions

Jenny opens a high-interest savings account where interest of $6.48%$6.48% per annum is compounded monthly. Her initial deposit is $\$12000$$12000 and she makes monthly deposits of \300$$300.

a

Complete the table below, rounding each answer to the nearest cent, and using the rounded answer to calculate the amounts for the following month.

 Month Balance at beginning of month ($\$$) Interest (\$$$) Deposit ($\$$) Balance at end of month (\$$$) 1 $12000$12000 $64.80$64.80 $300$300 $12364.80$12364.80 2 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ 3 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ 4 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ 5 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

For many investment accounts, interest is calculated daily, but paid into the account on a monthly basis. Choose the most accurate statement.

The interest earned over a year would be more since compounding more regularly results in faster exponential growth.

A

The interest earned over a year would be less since the daily interest rate would be a lot smaller.

B

The interest earned over a year would be the same.

C

The interest earned over a year would be more since compounding more regularly results in faster exponential growth.

A

The interest earned over a year would be less since the daily interest rate would be a lot smaller.

B

The interest earned over a year would be the same.

C
Easy
Approx 12 minutes

Bill has won $\$260000$$260000 and sets up an annuity earning 4.8%4.8% interest per annum, compounded annually. At the end of each year Bill withdraws \18000$$18000.

Mr and Mrs Lyne have a $\$520000$$520000 mortgage for their home. They are charged 5.16%5.16% interest per annum, compounded monthly and make monthly repayments of \3750$$3750.

Iain opens a savings account which earns interest of $12%$12% compounded quarterly. He also adds an additional deposit to his account each year. The balance of the investment, in dollars, at the end of each year where interest is compounded quarterly is given by$B_n=\left(1+0.03\right)^4\times B_{n-1}+4000$Bn=(1+0.03)4×Bn1+4000, where $B_0=22000$B0=22000.

### Outcomes

#### NA6-3

Apply everyday compounding rates

#### 91026

Apply numeric reasoning in solving problems