Question

An engaged couple agrees to get married once their savings equal $52,450.00. They have $26,200.00 at the moment and will invest the money in an account that earns 7.00% per year. How many years will the engagement last?

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Answer format: Number: Round to: 2 decimal places.

Answer 1

This problem can be solved by using the formula of simple interest or compound interest , as nothing is specifed we will use both the formulas , but compound interest would be more acurate as for the calculation , interest earned is added back to the principal amount and compounded there after.

• Solving by Simple Interest formula of A = P ( 1 + RT) { Where A is the furture value of the savings , P is the principal or savings today , R is the rate of interest and T is the time }
• In our problem T is unknown , let's put the known values and find out T
• The above formula can also be written as T = (1/R) * (A/P - 1 ) = (1 / 0.07) * (52450/26200 -1 ) = 14.28 Years

Therefore the couples have to wait 14.28 years to get married, that's too long.

Let us see If coumpound Interest helps us not , assuming the interest earned is invested back into the savings we will try to find out the time with the help of compound interest.

• The formula is A = P ( 1 + R ) ^N { A is the future value of investment , P is the principal amount or savings today ., R is the rate of interest , N is the number of years }
• By putting the values we get = 52450 = 26200 ( 1 + 0.07 ) ^ N = 2 = (1.07 ) ^N = 10.81 Years.

Thus , after 10.81 years the couples would be able to marry and their engagement has to last atleast a decade long as of now.