Answer to Question #263604 in Financial Math for qwer

Question

Joan has savings of $12000 on June 1. Since she may need some of the savings during the next 3 months she is considering two options at her bank. an Investment builder saving account earns a 2.25% rate of interest. The interest is calculated on the daily closing balance and paid on the first day of the following month. A 90- to 179- day cashable term deposit earns a rate of 2.8% paid at maturity. If interest rates do not change and Joan does not withdraw any of the funds how much more will she earn from the term deposit up to September 1? (Keep in mind that savings accounts interest paid on the first day of the month will itself subsequently earn interest during the subsequent month.)

Answer 1

Initial deposit=$12000

Interest rate=2.25%

Interest= number of days$\div$ 365 x interest rate x principal amount

Interest for June$=12000 \times 0.0225 \times \frac{30}{365}=\$22.1917808219$

Balance on last day of June$=12000+22.1917808219=\$12022.1917808219$

Interest for July$=12022.1917808219 \times \frac{31}{365} \times 0.0225=\$22.9739144305$

Balance on July End$=12022.1917808219+22.9739144305=\$12068.139609683$

Interest for August$=\frac{31}{365} \times 0.0225 \times 12068.139609683=\$23.0617188432$

Balance on 1 September$=12068.139609683+23.0617188432$

Balance on 1 September=$12091.20

Interest earned$=12091.20-12000=\$91.20$

Interest earned=$91.20

Option 2

Term deposit

Interest rate=2.8%

Number of days$=30+31+31=92 \space days$

Interest$= 0.028 \times \frac{92}{365} \times 12000=\$84.69$

More interest= Interest in daily basis- Interest in term deposit

More interest$=91.20-84.69=\$6.51$

That much more will she earn from the term deposit up to September 1.