Question

At age 20 a person deposits $370 in a savings account paying 2% interest compounded quaterly.how much money will be in the account 60 years later, when he is 80 years old? Would his savings have tripled in that time?

Answer 1

$1224.78 will be in the account 60 years later

Yes, his savings would have tripled in that time

Step-by-step explanation:

The formula for compound interest, including principal sum is

$A=P(1+\frac{r}{n})^{nt}$ where:

• A is the future value of the investment/loan, including interest
• P is the principal investment amount (the initial deposit or loan amount)
• r is the annual interest rate (decimal)
• n is the number of times that interest is compounded per unit t
• t is the time the money is invested or borrowed for

At age 20 a person deposits $370 in a savings account paying 2% interest compounded quarterly.

We need to find how much money will be in the account 60 years later, when he is 80 years old and would his savings have tripled in that time

∵ The deposit = $370

∴ P = 370

∵ The account paying 2% interest

∴ r = 2% = 2 ÷ 100 = 0.02

∵ The interest is compounded quarterly

∴ n = 4

∵ The money will be in the account 60 years later

∴ t = 60

By using the rule above

∴ $A=370(1+\frac{0.02}{4})^{(4)(60)}$

∴ $A=370(1+0.005)^{240}$

∴ $A=370(1.005)^{240}$

∴ A = 1224.78

$1224.78 will be in the account 60 years later

∵ A = 1224.78

∵ P = 370

∵ $\frac{A}{P}=\frac{1224.78}{370}=3.31$ ≅ 3

- That means A ≅ P × 3

∴ A approximately is 3 times P

Yes, his savings would have tripled in that time

Learn more:

You can learn more about compound interest in brainly.com/question/4361464

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