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QuestionBerapakah jumlah simpanan Puan Zainab selepas 5 tahun jika RM500 dideposit dengan faedah 4%4 \% setahun, dikompaun suku tahunan?

Studdy Solution

STEP 1

Assumptions1. The initial deposited amount is RM500. The interest rate is4% per annum3. The interest is compounded quarterly (every3 months)
4. We are interested in the total savings at the end of the fifth year

STEP 2

First, we need to find the quarterly interest rate. Since the interest is compounded quarterly, we divide the annual interest rate by4.
Quarterly interest rate=Annual interest rate/4Quarterly\, interest\, rate = Annual\, interest\, rate /4

STEP 3

Now, plug in the given value for the annual interest rate to calculate the quarterly interest rate.
Quarterly interest rate=%/Quarterly\, interest\, rate =\% /

STEP 4

Convert the percentage to a decimal value.
4%=0.044\% =0.04Quarterly interest rate=0.04/4Quarterly\, interest\, rate =0.04 /4

STEP 5

Calculate the quarterly interest rate.
Quarterly interest rate=0.04/4=0.01Quarterly\, interest\, rate =0.04 /4 =0.01

STEP 6

Now, we need to find the number of quarters in5 years. Since there are4 quarters in a year, we multiply the number of years by4.
Number of quarters=Number of yearstimes4Number\, of\, quarters = Number\, of\, years \\times4

STEP 7

Plug in the given value for the number of years to calculate the number of quarters.
Number of quarters=5times4Number\, of\, quarters =5 \\times4

STEP 8

Calculate the number of quarters.
Number of quarters=5times4=20Number\, of\, quarters =5 \\times4 =20

STEP 9

Now, we can calculate the total savings at the end of the fifth year using the formula for compound interest.
Total savings=Initial deposittimes(+Quarterly interest rate)Number of quartersTotal\, savings = Initial\, deposit \\times ( + Quarterly\, interest\, rate)^{Number\, of\, quarters}

STEP 10

Plug in the values for the initial deposit, quarterly interest rate, and number of quarters to calculate the total savings.
Total savings=RM500times(+0.01)20Total\, savings = RM500 \\times ( +0.01)^{20}

STEP 11

Calculate the total savings.
Total savings=RM500times(+0.01)20=RM610.51Total\, savings = RM500 \\times ( +0.01)^{20} = RM610.51uan Zainab's savings at the end of the fifth year will be RM610.51.

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