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3. A savings account is started with an initial deposit of $1500.The account earns 1.8% interest compounded annually.(a) Write an equation to represent the amount of money inthe account as a function of time in years. 5 Points(B) how much more interest would be earned if the initial deposit is allowed to earn interest for 20 years vs 10 years

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a) We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

where

A = the total amount in the account at the end of t years

r = interest rate

n = the periodic interval at which it was compounded

P = the principal or initial amount deposited

From the information given,

P = 1500

r = 1.8/100 = 0.018

n = 1 because it is compounded once in a year

Thus, an equation to represent the amount of money in the account as a function of time in years ia

A = 1500(1 + 0.018/1)^1 * t

A = 1500(1.018)^t

B) If t = 20, then

A = 1500(1.018)^20

A = 2143.12

The interest earned would be the total amount - the principal

Interest earned after 20 years = 2143.12 - 1500 = 643.12

If t = 10, then

A = 1500(1.018)^10

A = 1792.95

Interest earned after 10 years = 1792.95 - 1500 = 292.95

Thus, the difference in interest earned between both years is

643.12 - 292.95

= $350.17

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